From f2339b20aa6ed90f5d7135d852cabe05d0267476 Mon Sep 17 00:00:00 2001 From: Reinhold Kainhofer <reinhold@kainhofer.com> Date: Fri, 15 Apr 2016 00:04:58 +0200 Subject: [PATCH] Lots of improvements - Implement terme fixe - Lots more loadings and rebates - fix some issues with premium and present value calculation - Calculate total benefix present value (survival, death, premium refund) - Loadings can be overridden in the contract object (passed to the tarif, where the tarif-wide and contract-specific loadings are merged and contract-specific settings take precedence) - First attempt at reserve calcultion - Move contract class to its own file - Valuation Tables: add modification function to adjust resulting death probabilities (e.g. monotonize, set lower bound for q_x, etc.) - Properly implement age-shifted tables, add ageShift(table, YOB) function --- .../Formelsammlung_Beispielrechnung.pdf | Bin 219429 -> 221399 bytes .../Formelsammlung_Beispielrechnung.tex | 22 +- R/InsuranceContract.R | 263 +++++++--------- R/InsuranceTarif.R | 285 +++++++----------- R/ValuationTables.R | 70 +++-- R/ValuationTables_Austria_Annuities.R | 1 + R/ValuationTables_Austria_Census.R | 10 +- 7 files changed, 296 insertions(+), 355 deletions(-) diff --git a/Formulas_Reference/Formelsammlung_Beispielrechnung.pdf b/Formulas_Reference/Formelsammlung_Beispielrechnung.pdf index 0fe614cc66984ad456a22bbce29c30e379a86dc0..105f4b4c6cd5eacdebfe1a8419048aca6ca26b3f 100644 GIT binary patch delta 60462 zcmZ3wiTC<J-VFwf^`}(|jrP^vzRDXnYfA94xsjDY6P${B-BRZ?+D56(yzt@m+g)q6 zg>GlG-xrs%N8^(AYR}-LjCm<jJQVL9vVY4xi>3e6+otC)FF05@ynfrXR8+ztvnsMo z{zK?h-l@W`^QVWtez!YobF;<1@^XQMn!Eg8uXWZunx}s{nrEVTf)itX>g9@y=f!s3 zKIVGt5?fEkT*1<U&TXY;w+gOXI!Erh`7n74Q|k8M!Z_dE>x^DknjJgxc60ZEU7wb1 zXQ?+$P#4b(H9vQMm%DWF<hm8RmqrJ?t11uNu6-ehZ-s67t%ol^pVLaV)DoP?+n|2u zMS*zP+oC^Jk&AS+Kgh|x`SW;Jk$C+EzQwoqzg=ZsQJQ`Df|JO!dly#UEsKskz3P}W zkD$elpDFqqzZ<z<_o)ikb<}RTbok(`?s*v}_ITd7b!+AJYX_Eb%(Qz`P~PIvUi9Ma 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zrTMsYUfy&z_oAMa%kqwHy^Fe4F6&<i|5Z|CJF-AR=&;Mrt9G+g<}C`-d}N(GRV}!3 zwcw{W_p+w!`ME(#S-U^%@ssBhud>{|xAUsXUDs<_UGLPt9n6~b&N5}{!qqjAXD@L7 v`TtaB?~?Obes4Nrt6IG;X#ah{Z}ULw@AP#E%(6U&78d3fT&k+B{%%|VLIrYF diff --git a/Formulas_Reference/Formelsammlung_Beispielrechnung.tex b/Formulas_Reference/Formelsammlung_Beispielrechnung.tex index 81ef653..afe4691 100644 --- a/Formulas_Reference/Formelsammlung_Beispielrechnung.tex +++ b/Formulas_Reference/Formelsammlung_Beispielrechnung.tex @@ -577,24 +577,30 @@ Bruttoprämie & Zähler & \section{Zuschläge und Abschläge, Vorgeschriebene Prämie} \begin{longtable}{p{4cm}p{11cm}} - $StkK$ \dots & Stückkosten pro Jahr (während Prämienzahlungsdauer, einmalig bei Einmalprämien)\\ $oUZu$ \dots & Zuschlag für Vertrag ohne ärztliche Untersuchung\\ $SuRa=SuRa(VS)$ \dots & Summenrabatt (von Höhe der VS abhängig)\\ + $VwGew$ \dots & Vorweggewinnbeteiligung in Form eines \%-uellen Rabattes auf die Bruttoprämie\\ + $StkK$ \dots & Stückkosten pro Jahr (während Prämienzahlungsdauer, einmalig bei Einmalprämien)\\ $PrRa=PrRa(BP)$ \dots & Prämienrabatt (von Höhe der Bruttoprämie abhängig)\\ - $VwGew$ \dots & Vorweggewinnbeteiligung in Form eines Rabattes\\ + $VwGew_{StkK}$ \dots & Vorweggewinnbeteiligung in Form eines Rabattes auf die Prämie nach Zu-/Abschlägen (insbesondere nach Stückkosten)\\ + $PartnerRa$ \dots & Partnerrabatt auf Prämie nach Zu-/Abschlägen (z.B. bei Abschluss mehrerer Verträge), additiv zu $VwGew_{StkK}$\\ + $uz(k)$ \dots & Zuschlag für unterjährige Prämienzahlung ($k$ mal pro Jahr) \begin{equation*} - uz(k)= - \end{equation*} + uz(k)=\left.\begin{cases}uk_1 & \text {für jährliche}\\uk_2 & \text {für halbjährliche} \\ uk_4 & \text{für quartalsweise}\\uk_{12} & \text{für monatliche}\end{cases}\right\} \text{Prämienzahlung} + \end{equation*}\\ + + + $VSt$ \dots & Versicherungssteuer (in Österreich 4\% oder 11\%) \\ \end{longtable} -\begin{align*} -\intertext{Vorgeschriebene Prämie:} -PV_{\act[x]{n}} &= \left\{ (BP_{\act[x]{n}} + oUZu - SuRa) \cdot VS \cdot (1-VwGew) + StkK\right\} \cdot \frac{1+uz(pz)}{pz} \cdot (1+VSt) +Vorgeschriebene Prämie: +\begin{multline*} +PV_{\act[x]{n}} = \left\{ (BP_{\act[x]{n}} + oUZu - SuRa) \cdot VS \cdot (1-VwGew) + StkK\right\} \cdot \\ \left(1-PrRa-VwGew_{StkK}-PartnerRa\right)\cdot \frac{1+uz(k)}{k} \cdot (1+VSt) % -\end{align*} +\end{multline*} \pagebreak diff --git a/R/InsuranceContract.R b/R/InsuranceContract.R index 016450b..79f0b41 100644 --- a/R/InsuranceContract.R +++ b/R/InsuranceContract.R @@ -1,154 +1,113 @@ -library("lifecontingencies"); - - -# (virtual) base class for valuation tables, contains only the name / ID -InsuranceContract=setRefClass( - "InsuranceContract", - slots=c( - name="character", - tarif="character", - desc="character", - YOB="numeric", - YOB2="numeric", - age="numeric", - age2="numeric", - contractLength="numeric", - mortalityTable="valuationTable", - mortalityTable2="valuationTable", - - interest="numeric", - -# cashflows="data.frame", -# deathPayments="list", -# survivalPayments="list", -# costCashflows="data.frame", - cashflows="data.frame", - - probabilities="data.frame", - - - unterjährigkeit="numeric", - unterjährigkeitsapproximation="numeric", - cache.uj="list" - - - ), - prototype=list( - name="Insurance Contract Type", - tarif="Tariff", - desc="Description of the contract", - YOB=1977, -# YOB2=1977, - age=35, -# age2=35, - contractLength=Inf, - mortalityTable=AVOe2005R.unisex, -# mortalityTable2=AVOe2005R.unisex, - - interest=0, - - deathPayments=list(), - survivalPayments=list(), - costCashflows=data.frame(), - cashflows=data.frame(), - probabilities=data.frame(), - - unterjährigkeit=1, - unterjährigkeitsapproximation=1 - ) -); -# createCostStructure=function(age=35,contractLength=inf, -# alphaVS, -# alphaBP, -# -# -# CostStructure=setClass( -# "CostStructure", -# -# ) - - -calcUnterjährigkeit = function(m=1,i=0, order=0) { - alpha=1; - beta=(m-1)/(2*m); - if (order>=1) { beta = beta + (m^2-1)/(6*m^2)*i; } - if (order == 1.5) { beta = beta + (1-m^2)/(12*m^2)*i^2; } - if (order >= 2) { beta = beta + (1-m^2)/(24*m^2)*i^2; - alpha= alpha+ (m^2-1)/(12*m^2)*i^2; } - list(alpha=alpha, beta=beta); -} - -setGeneric("createContractCashflows", function(object) standardGeneric("createContractCashflows")) - -setGeneric("calculate", function(object) standardGeneric("calculate")); -setMethod("calculate", "InsuranceContract", - function (object) { - # 0) Prepare helper values - # 0a: Unterjährigkeit - m = object@unterjährigkeit; - object@cache.uj=calcUnterjährigkeit(m=m, i=object@interest, order=object@unterjährigkeitsapproximation); - - - # 1) Generate mortality table - if (!is.null(object@contractLength) && is.finite(object@contractLength)) { - ages = (object@age):(object@contractLength); - } else { - ages = (object@age):150; - } - qx = deathProbabilities(object@mortalityTable, YOB=object@YOB)[ages+1]; - pxn = cumprod(1-qx); - object@probabilities = data.frame(ages=ages,qx=qx, pxn=pxn) - if (!is.null(object@YOB2)) { - ages2 = ages - object@age + object@age2; - qx2 = deathProbabilities(object@mortalityTable2, YOB=object@YOB2)[ages2+1]; - pxn2 = cumprod(1-qx2); - pxyn = pxn * pxn2; - object@probabilities = data.frame(object@probabilities, ages2=ages2, q2=qx2, pxn2=pxn2, pxyn=pxyn); - } - - - # 2) Properly set up the payment and cost cash flow data frames - - # 3) Calculate all NPVs of the payment and the cost cash flows (recursively) - # 3a: life-long annuities for person 2 (and person 1+2), in case the death benefit is a life-long widow's annuity - - # 4) Set up the coefficients of the NPVs for the premium calculation - - # 5) Calculate the gross premium - # 6) Calculate the net premium and the Zillmer premium - - # 7) Calculate all reserves (benefits and costs) - - # 8) Calculate Spar- und Risikoprämie from the net premium and the reserves - - # 9) Calculate VS after Prämienfreistellung - # 9a: Calculate all reserves after Prämienfreistellung - - # 10) Calculate the Bilanz reserves - - # 11) Calculate the Rückkaufswert -# max(object@ages,na.rm=TRUE); - object -}) - - -beispielvertrag = InsuranceContract( - name="Beispielvertrag", tarif="Beispieltarif", - desc="Beispiel zum Testen des Codes", - YOB=1948, YOB2=1948+65-62, - age=65, age2=62, -# contractLength=30, - mortalityTable=AVOe2005R.unisex, mortalityTable2=AVOe2005R.unisex, - interest=0.0125, - - unterjährigkeit=12, unterjährigkeitsapproximation=1.5, - -# deathPayments=list(), -# survivalPayments=list(), -# costCashflows=data.frame(), -# cashflows=data.frame() +InsuranceContract = R6Class( + "InsuranceContract", + public = list( + tarif = NA, + + #### Contract settings + sumInsured = 1, + YOB = NA, + age = NA, + policyPeriod = Inf, + premiumPeriod = 1, + deferral = 0, + guaranteed = 0, + + premiumPayments = PaymentTimeEnum("in advance"), + benefitPayments = PaymentTimeEnum("in advance"), + + premiumFrequency = 1, + benefitFrequency = 1, # Only for annuities! + + loadings = list(), # Allow overriding the tariff-defined loadings (see the InsuranceTariff class for all possible names) + + #### Caching values for this contract, initialized/calculated when the object is created + transitionProbabilities = NA, + + cashFlowsBasic = NA, + cashFlows = NA, + cashFlowsCosts = NA, + premiumSum = 0, + + presentValues = NA, + presentValuesCosts = NA, + + premiums = NA, + reserves = NA, + + + #### The code: + + initialize = function(tarif, age, policyPeriod, + premiumPeriod = policyPeriod, sumInsured = 1, + ..., + loadings = list(), + guaranteed = 0, + premiumPayments = "in advance", benefitPayments = "in advance", + premiumFrequency = 1, benefitFrequency = 1, + deferral = 0, YOB = 1975) { + self$tarif = tarif; + self$age = age; + self$policyPeriod = policyPeriod; + self$premiumPeriod = premiumPeriod; + self$sumInsured = sumInsured; + if (!missing(deferral)) self$deferral = deferral; + if (!missing(YOB)) self$YOB = YOB; + if (!missing(premiumPayments)) self$premiumPayments = premiumPayments; + if (!missing(benefitPayments)) self$benefitPayments = benefitPayments; + if (!missing(premiumFrequency)) self$premiumFrequency = premiumFrequency; + if (!missing(benefitFrequency)) self$benefitFrequency = benefitFrequency; + if (!missing(guaranteed)) self$guaranteed = guaranteed; + if (!missing(loadings)) self$loadings = loadings; + + self$recalculate(); + }, + + recalculate = function() { + self$determineTransitionProbabilities(); + self$determineCashFlows(); + self$calculatePresentValues(); + self$calculatePremiums(); + self$calculatePresentValuesAllBenefits(); + self$calculateReserves(); + + }, + + determineTransitionProbabilities = function() { + self$transitionProbabilities = self$tarif$getTransitionProbabilities(YOB = self$YOB, age = self$age); + self$transitionProbabilities + }, + + determineCashFlows = function() { + self$cashFlowsBasic = self$tarif$getBasicCashFlows(YOB = self$YOB, age = self$age, guaranteed = self$guaranteed, deferral = self$deferral, policyPeriod = self$policyPeriod, premiumPeriod = self$premiumPeriod); + self$cashFlows = self$tarif$getCashFlows(age = self$age, premiumPayments = self$premiumPayments, benefitPayments = self$benefitPayments, policyPeriod = self$policyPeriod, guaranteed = self$guaranteed, deferral = self$deferral, premiumPaymentPeriod = self$premiumPeriod, basicCashFlows = self$cashFlowsBasic); + self$premiumSum = sum(self$cashFlows$premiums_advance + self$cashFlows$premiums_arrears); + self$cashFlowsCosts = self$tarif$getCashFlowsCosts(YOB = self$YOB, age = self$age, deferral = self$deferral, guaranteed = self$guaranteed, premiumPaymentPeriod = self$premiumPeriod, policyPeriod = self$policyPeriod); + list("benefits"= self$cashFlows, "costs"=self$cashFlowCosts, "premiumSum" = self$premiumSum) + }, + + calculatePresentValues = function() { + self$presentValues = self$tarif$presentValueCashFlows(self$cashFlows, age = self$age, YOB = self$YOB, premiumFrequency = self$premiumFrequency, benefitFrequency = self$benefitFrequency, loadings = self$loadings); + self$presentValuesCosts = self$tarif$presentValueCashFlowsCosts(self$cashFlowsCosts, age = self$age, YOB = self$YOB); + list("benefits" = self$presentValues, "costs" = self$presentValuesCosts) + }, + + # Add total benefits present value to the PV array. This can only be done after premium calculation, because e.g. premium refund depends on gross premium! + calculatePresentValuesAllBenefits = function() { + pvAllBenefits = self$tarif$presentValueBenefits(presentValues = self$presentValues, premiums = self$premiums, sumInsured = self$sumInsured); + self$presentValues = cbind(self$presentValues, pvAllBenefits) + self$presentValues + }, + + calculatePremiums = function() { + self$premiums = self$tarif$premiumCalculation(self$presentValues, self$presentValuesCosts, premiumSum = self$premiumSum, sumInsured = self$sumInsured, loadings = self$loadings); + self$premiums + }, + + calculateReserves = function() { + self$reserves = self$tarif$reserveCalculation(premiums=self$premiums, pvBenefits=self$presentValues, pvCosts=self$presentValuesCosts, sumInsured=self$sumInsured, loadings = self$loadings); + }, + + dummy=NA + ) ); -beispielvertrag=calculate(beispielvertrag) -beispielvertrag -# data.frame(x=0:121, qx=deathProbabilities(AVOe2005R.unisex, YOB=1948)) \ No newline at end of file diff --git a/R/InsuranceTarif.R b/R/InsuranceTarif.R index 32e537f..b43c8cb 100644 --- a/R/InsuranceTarif.R +++ b/R/InsuranceTarif.R @@ -3,7 +3,7 @@ library(lifecontingencies) library(objectProperties) library(foreach) -TariffTypeEnum = setSingleEnum("TariffType", levels = c("annuity", "wholelife", "endowment", "pureendowment")) +TariffTypeEnum = setSingleEnum("TariffType", levels = c("annuity", "wholelife", "endowment", "pureendowment", "terme-fix")) PaymentTimeEnum = setSingleEnum("PaymentTime", levels = c("in advance", "in arrears")) #PaymentCountEnum = setSingleEnum(PaymentCount, levels = c(1,2,3)) @@ -21,7 +21,7 @@ initializeCosts = function() { ); array(0, dim=sapply(dimnm, length), - dimnames=dimnames + dimnames=dimnm ) } @@ -41,7 +41,7 @@ InsuranceTarif = R6Class( mortalityTable = NA, i = 0, # guaranteed interest rate v = 1, # discount factor - tariffType = TariffTypeEnum("wholelife"), # possible values: annuity, wholelife, endowment, pureendowment + tariffType = TariffTypeEnum("wholelife"), # possible values: annuity, wholelife, endowment, pureendowment, terme-fix premiumFrequencyOrder = 0, benefitFrequencyOrder = 0, widowFactor = 0, @@ -49,21 +49,21 @@ InsuranceTarif = R6Class( premiumRefund = 0, premiumRefundLoading = 0, # Mindesttodesfallrisiko soll damit erreicht werden, z.B. 105% der einbezahlten Prämien - advanceBonus = 0, - sumRebate = 0, - costs = list(), benefitFrequencyLoading = list("1" = 0.0, "2" = 0.0, "4" = 0.0, "12" = 0.0), # TODO: Properly implement this premiumFrequencyLoading = list("1" = 0.0, "2" = 0.0, "4" = 0.0, "12" = 0.0), # TODO: Implement this loadings = list( # Loadings can also be function(sumInsured, premiums) # TODO: Add other possible arguments + "ongoingAlphaGrossPremium" = 0, # Acquisition cost that increase the gross premium "tax" = 0.04, # insurance tax, factor on each premium paid "unitcosts" = 0, # annual unit cost for each policy (Stückkosten), absolute value "security" = 0, # Additional security loading on all benefit payments, factor on all benefits "noMedicalExam" = 0, # Loading when no medicial exam is done, % of SumInsured + "noMedicalExamRelative" = 0, # Loading when no medicial exam is done, % of gross premium "sumRebate" = 0, # gross premium reduction for large premiums, % of SumInsured "premiumRebate" = 0, # gross premium reduction for large premiums, % of gross premium # TODO - "advanceProfitParticipation" = 0, # Profit participation in advance, % of the premium - "ongoingAlphaGrossPremium" = 0 # Acquisition cost that increase the gross premium + "advanceProfitParticipation" = 0, # Vorweggewinnbeteiligung (%-Satz der Bruttoprämie) + "advanceProfitParticipationInclUnitCost" = 0, # Vorweggewinnbeteiligung (%-Satz der Prämie mit Zu-/Abschlägen, insbesondere nach Stückkosten) + "partnerRebate" = 0 # Partnerrabatt auf Prämie mit Zu-/Abschlägen, wenn mehr als 1 Vertrag gleichzeitig abgeschlossen wird, additiv mit advanceBonusInclUnitCost and premiumRebate ), @@ -101,7 +101,6 @@ InsuranceTarif = R6Class( }, getBasicCashFlows = function(age, ..., guaranteed = 0, policyPeriod = inf, deferral = 0, maxAge = getOmega(self$mortalityTable)) { maxlen = min(maxAge - age, policyPeriod); - cf = list( guaranteed = rep(0, maxlen+1), survival = rep(0, maxlen+1), @@ -110,7 +109,9 @@ InsuranceTarif = R6Class( if (self$tariffType == "annuity") { # guaranteed payments exist only with annuities (first n years of the payment) cf$guaranteed = c(rep(0, deferral), rep(1, guaranteed), rep(0, max(0, maxlen+1 - deferral - guaranteed))) - cf$survival = c(rep(0, deferral + guaranteed), rep(1, max(0, maxlen+1 - deferral - guaranteed))) + cf$survival = c(rep(0, deferral + guaranteed), rep(1, max(0, maxlen - deferral - guaranteed)), 0) + } else if (self$tariffType == "terme-fix") { + cf$guaranteed = c(rep(0, policyPeriod), 1); } else { if (self$tariffType == "endowment" || self$tariffType == "pureendowment") { cf$survival = c(rep(0, policyPeriod), 1); @@ -205,17 +206,17 @@ InsuranceTarif = R6Class( benefitFrequencyCorrection = correctionPaymentFrequency(m = benefitFrequency, i = self$i, order = self$benefitFrequencyOrder); premiumFrequencyCorrection = correctionPaymentFrequency(m = premiumFrequency, i = self$i, order = self$premiumFrequencyOrder); - pv = as.matrix(data.frame( # TODO: Find a better way to combine the vectors into a matrix with given row/column names! + # pv = as.matrix(data.frame( # TODO: Find a better way to combine the vectors into a matrix with given row/column names! + pv = (cbind( # TODO: Find a better way to combine the vectors into a matrix with given row/column names! age = ages, premiums = calculatePVSurvival (q, cashflows$premiums_advance, cashflows$premiums_arrears, m=premiumFrequency, mCorrection=premiumFrequencyCorrection, v=self$v), guaranteed = calculatePVSurvival (q*0, cashflows$guaranteed_advance, cashflows$guaranteed_arrears, m=benefitFrequency, mCorrection=benefitFrequencyCorrection, v=self$v), survival = calculatePVSurvival (q, cashflows$survival_advance, cashflows$survival_arrears, m=benefitFrequency, mCorrection=benefitFrequencyCorrection, v=self$v), death_SumInsured = calculatePVDeath (q, cashflows$death_SumInsured, v=self$v), death_GrossPremium = calculatePVDeath (q, cashflows$death_GrossPremium, v=self$v), - death_PremiumFree = calculatePVDeath (q, cashflows$death_PremiumFree, v=self$v), - - row.names = pad0(rownames(qq), len) + death_PremiumFree = calculatePVDeath (q, cashflows$death_PremiumFree, v=self$v) )); + rownames(pv) <- pad0(rownames(qq), len); pv }, @@ -228,10 +229,18 @@ InsuranceTarif = R6Class( pvc }, + presentValueBenefits = function(presentValues, premiums, sumInsured=1) { + benefits.unit = presentValues[,"survival"] + presentValues[,"death_SumInsured"]; + benefits = benefits.unit * sumInsured; + allBenefits.unit = presentValues[,"survival"] + presentValues[,"death_SumInsured"] + presentValues[,"death_GrossPremium"] * premiums[["unit.gross"]]; + allBenefits = allBenefits.unit * sumInsured; + cbind(benefits.unit=benefits.unit, benefits=benefits, allBenefits.unit=allBenefits.unit, allBenefits=allBenefits) + }, + getPremiumCoefficients = function(type="gross", coeffBenefits, coeffCosts, ..., - premiumSum = 0, + loadings = self$loadings, premiumSum = 0, premiums = c("unit.gross"=0)) { - securityLoading = self$loadings$security; + securityLoading = loadings$security; refundAddon = self$premiumRefundLoading; coefficients = list( @@ -284,11 +293,14 @@ InsuranceTarif = R6Class( coefficients }, - premiumCalculation = function(pvBenefits, pvCosts, costs=self$costs, premiumSum=0, sumInsured=1, premiumFrequency = 1) { - premiums = c("unit.net" = 0, "unit.gross"= 0, "unit.Zillmer" = 0, "net" = 0, "gross" = 0, "Zillmer" = 0, "written" = 0); + premiumCalculation = function(pvBenefits, pvCosts, costs=self$costs, premiumSum=0, sumInsured=1, premiumFrequency = 1, loadings=list(), ...) { + # The loadings passed to this function override the tariff settings! + loadings = c(loadings, self$loadings); +str(loadings); + premiums = c("unit.net" = 0, "unit.Zillmer" = 0, "unit.gross"= 0, "net" = 0, "Zillmer" = 0, "gross" = 0, "written" = 0); # net, gross and Zillmer premiums are calculated from the present values using the coefficients on each present value as described in the formulas document - coeff=self$getPremiumCoefficients("gross", pvBenefits["0",]*0, pvCosts["0",,]*0, premiums=premiums, premiumSum=premiumSum) + coeff=self$getPremiumCoefficients("gross", pvBenefits["0",]*0, pvCosts["0",,]*0, premiums=premiums, premiumSum=premiumSum, loadings=loadings) enumerator = sum(coeff[["SumInsured"]][["benefits"]] * pvBenefits["0",]) + sum(coeff[["SumInsured"]][["costs"]] * pvCosts["0",,]); denominator = sum(coeff[["Premium" ]][["benefits"]] * pvBenefits["0",]) + sum(coeff[["Premium" ]][["costs"]] * pvCosts["0",,]); ongoingAlphaGrossPremium = self$loadings$ongoingAlphaGrossPremium; @@ -307,18 +319,31 @@ InsuranceTarif = R6Class( premiums[["unit.Zillmer"]] = enumerator/denominator; premiums[["Zillmer"]] = premiums[["unit.Zillmer"]] * sumInsured; + # The written premium is the gross premium with additional loadings, rebates, unit costs and taxes - tax = valueOrFunction(self$loadings$tax, sumInsured=sumInsured, premiums=premiums); - unitCosts = valueOrFunction(self$loadings$unitcosts, sumInsured=sumInsured, premiums=premiums); - noMedicalExam = valueOrFunction(self$loadings$noMedicalExam,sumInsured=sumInsured, premiums=premiums); - sumRebate = valueOrFunction(self$loadings$sumRebate, sumInsured=sumInsured, premiums=premiums); - premiumRebate = valueOrFunction(self$loadings$premiumRebate,sumInsured=sumInsured, premiums=premiums); # TODO: How shall this be included in the premium calculation? - advanceProfitParticipation = valueOrFunction(self$loadings$advanceProfitParticipation,sumInsured=sumInsured, premiums=premiums); + tax = valueOrFunction(loadings$tax, sumInsured=sumInsured, premiums=premiums); + unitCosts = valueOrFunction(loadings$unitcosts, sumInsured=sumInsured, premiums=premiums); + noMedicalExam = valueOrFunction(loadings$noMedicalExam,sumInsured=sumInsured, premiums=premiums); + noMedicalExam.relative = valueOrFunction(loadings$noMedicalExamRelative,sumInsured=sumInsured, premiums=premiums); + sumRebate = valueOrFunction(loadings$sumRebate, sumInsured=sumInsured, premiums=premiums); + premiumRebate = valueOrFunction(loadings$premiumRebate,sumInsured=sumInsured, premiums=premiums); + advanceProfitParticipation = valueOrFunction(loadings$advanceProfitParticipation,sumInsured=sumInsured, premiums=premiums); + advanceProfitParticipationUnitCosts = valueOrFunction(loadings$advanceProfitParticipationInclUnitCost, sumInsured=sumInsured, premiums=premiums); + partnerRebate = valueOrFunction(loadings$partnerRebate,sumInsured=sumInsured, premiums=premiums); frequencyLoading = valueOrFunction(self$premiumFrequencyLoading, sumInsured=sumInsured, premiums=premiums); - premiumBeforeTax = (premiums[["unit.gross"]] + noMedicalExam - sumRebate)*sumInsured * (1-advanceProfitParticipation) + unitCosts; +str(premiums[["unit.gross"]]*(1+noMedicalExam.relative) + noMedicalExam - sumRebate); +str(sumInsured); +str(1-advanceProfitParticipation); +str(unitCosts); + + premiumBeforeTax = (premiums[["unit.gross"]]*(1+noMedicalExam.relative) + noMedicalExam - sumRebate)*sumInsured * (1-advanceProfitParticipation) + unitCosts; +str(premiumBeforeTax); + premiumBeforeTax = premiumBeforeTax * (1-premiumRebate-advanceProfitParticipationUnitCosts-partnerRebate); +str(premiumBeforeTax); premiumBeforeTax = premiumBeforeTax * (1+frequencyLoading[[toString(premiumFrequency)]]) / premiumFrequency; +str(premiumBeforeTax); premiums[["written_beforetax"]] = premiumBeforeTax; premiums[["tax"]] = premiumBeforeTax * tax; premiums[["written"]] = premiumBeforeTax * (1 + tax); @@ -326,155 +351,77 @@ InsuranceTarif = R6Class( premiums }, + reserveCalculation = function (premiums, pvBenefits, pvCosts, sumInsured=1, ...) { + resZ = pvBenefits[,"allBenefits"]*(1+self$loadings$security) - premiums[["Zillmer"]] * pvBenefits[,"premiums"]; + res.gamma = (pvCosts[,"gamma", "SumInsured"] - pvCosts["0", "gamma", "SumInsured"]/pvBenefits["0", "premiums"]*pvBenefits[,"premiums"])*sumInsured; + # res.premiumfree = + # res.gamma.premiumfree = - # Dummy to allow commas - dummy = 0 - ) -); - - -costs = initializeCosts(); -# costs["alpha", "SumInsured",] = c(1,2,5); -# costs["beta", "SumPremiums",] = c(3,2,1); -costs["alpha", "SumPremiums", "once"] = 0.05; -costs["Zillmer", "SumPremiums", "once"] = 0.04; -costs["gamma", "SumInsured", "PremiumPeriod"] = 0.005; -costs["gamma", "SumInsured", "PremiumFree"] = 0.01; -costs["gamma_nopremiums", "SumInsured", "PolicyPeriod"] = 0.01; - -costs - -TestTarif = InsuranceTarif$new(name = "Testtarif", mortalityTable = AVOe2005R.male, type = "annuity", costs=costs) -q = TestTarif$getTransitionProbabilities(YOB = 1980, age = 30) -TestTarif = InsuranceTarif$new(name = "Testtarif", mortalityTable = AVOe2005R.male, type = "wholelife", costs=costs) -TestTarif$getBasicCashFlows(YOB = 1980, age = 30, policyPeriod = 5, deferral = 3, guaranteed=10) - -# Gemischte Versicherung, i=1%, AVÖ2005R Unisex, YOB=1980, age=30, Laufzeit=10, Prämienzahlungsdauer=5, -TestTarif = InsuranceTarif$new(name = "Testtarif", mortalityTable = AVOe2005R.unisex, type = "endowment", costs=costs, i=0.01) -TestTarif$getBasicCashFlows(YOB = 1980, age = 30, premiumPaymentPeriod = 5, policyPeriod = 10, deferral = 0, guaranteed=0) - -TestTarif$costs=costs; -TestTarif$premiumRefund = 0; - -cf = TestTarif$getCashFlows(YOB = 1980, age = 30, premiumPaymentPeriod = 5, policyPeriod = 10, deferral = 0, guaranteed=0); cf -cfc = TestTarif$getCashFlowsCosts(YOB = 1980, age = 30, premiumPaymentPeriod = 5, policyPeriod = 10, deferral = 0, guaranteed=0); cfc - -pv = TestTarif$presentValueCashFlows(cf, age = 30, YOB=1980); pv -pvc = TestTarif$presentValueCashFlowsCosts(cfc, age=30, YOB=1980); pvc - -premiums=TestTarif$premiumCalculation(pv, pvc, premiumSum=15); premiums - - - -premiums*1000 -as.array(premiums)*1000 - -c("net"=1, "gross"=23, "Zillmer"=44) -str(as.matrix( premiums)) -as.matrix(premiums)*1000 -scf -cfc -dim(cfc)[1] - -str(cf$premiums_advance) -calculatePVSurvival(q$q, cf$premiums_advance, cf$premiums_arrears, v=1/1.01) -calculatePVSurvival(q$q, cf$survival_advance, cf$survival_arrears, v=1/1.01) - -calculatePVDeath(q$q, cf$death_SumInsured, v=1/1.01) -calculatePVDeath(q$q, cf$death_GrossPremium, v=1/1.01) -calculatePVDeath(q$q, cf$death_PremiumFree, v=1/1.01) - - - -InsuranceContract = R6Class( - "InsuranceContract", - public = list( - tarif = NA, - - #### Contract settings - sumInsured = 1, - YOB = NA, - age = NA, - policyPeriod = Inf, - premiumPeriod = 1, - deferral = 0, - guaranteed = 0, - - premiumPayments = PaymentTimeEnum("in advance"), - benefitPayments = PaymentTimeEnum("in advance"), - - premiumFrequency = 1, - benefitFrequency = 1, # Only for annuities! - - #### Caching values for this contract, initialized/calculated when the object is created - transitionProbabilities = NA, - - cashFlowsBasic = NA, - cashFlows = NA, - cashFlowsCosts = NA, - premiumSum = 0, - - presentValues = NA, - presentValuesCosts = NA, - - premiums = NA, - - - #### The code: - - initialize = function(tarif, age, policyPeriod, - premiumPeriod = policyPeriod, sumInsured = 1, - ..., - premiumPayments = "in advance", benefitPayments = "in advance", - premiumFrequency = 1, benefitFrequency = 1, - deferral = 0, YOB = 1975) { - self$tarif = tarif; - self$age = age; - self$policyPeriod = policyPeriod; - self$premiumPeriod = premiumPeriod; - self$sumInsured = sumInsured; - if (!missing(deferral)) self$deferral = deferral; - if (!missing(YOB)) self$YOB = YOB; - if (!missing(premiumPayments)) self$premiumPayments = premiumPayments; - if (!missing(benefitPayments)) self$benefitPayments = benefitPayments; - if (!missing(premiumFrequency)) self$premiumFrequency = premiumFrequency; - if (!missing(benefitFrequency)) self$benefitFrequency = benefitFrequency; - - self$determineTransitionProbabilities(); - self$determineCashFlows(); - self$calculatePresentValues(); - self$calculatePremiums(); + res = cbind("Reserve"=resZ, "Reserve.gamma"=res.gamma#, "Reserve.premiumfree"=res.premiumfree, "Reserve.gamma.premiumfree"=res.gamma.premiumfree); + ); + rownames(res) <- rownames(pvBenefits); + res }, - determineTransitionProbabilities = function() { - self$transitionProbabilities = self$tarif$getTransitionProbabilities(YOB = self$YOB, age = self$age); - self$transitionProbabilities - }, - determineCashFlows = function() { - self$cashFlowsBasic = self$tarif$getBasicCashFlows(YOB = self$YOB, age = self$age, policyPeriod = self$policyPeriod, premiumPeriod = self$premiumPeriod); - self$cashFlows = self$tarif$getCashFlows(age = self$age, premiumPayments = self$premiumPayments, benefitPayments = self$benefitPayments, policyPeriod = self$policyPeriod, premiumPaymentPeriod = self$premiumPeriod, basicCashFlows = self$cashFlowsBasic); - self$premiumSum = sum(self$cashFlows$premiums_advance + self$cashFlows$premiums_arrears); - self$cashFlowsCosts = self$tarif$getCashFlowsCosts(YOB = self$YOB, age = self$age, premiumPaymentPeriod = self$premiumPeriod, policyPeriod = self$policyPeriod); - list("benefits"= self$cashFlows, "costs"=self$cashFlowCosts, "premiumSum" = self$premiumSum) - }, - calculatePresentValues = function() { - self$presentValues = self$tarif$presentValueCashFlows(self$cashFlows, age = self$age, YOB = self$YOB, premiumFrequency = self$premiumFrequency, benefitFrequency = self$benefitFrequency); - self$presentValuesCosts = self$tarif$presentValueCashFlowsCosts(self$cashFlowsCosts, age = self$age, YOB = self$YOB); - list("benefits" = self$presentValues, "costs" = self$presentValuesCosts) - }, - - calculatePremiums = function() { - self$premiums = self$tarif$premiumCalculation(self$presentValues, self$presentValuesCosts, premiumSum = self$premiumSum, sumInsured = self$sumInsured); - self$premiums - }, - dummy=NA + # Dummy to allow commas + dummy = 0 ) ); - - - - +# +# +# costs = initializeCosts(); +# # costs["alpha", "SumInsured",] = c(1,2,5); +# # costs["beta", "SumPremiums",] = c(3,2,1); +# costs["alpha", "SumPremiums", "once"] = 0.05; +# costs["Zillmer", "SumPremiums", "once"] = 0.04; +# costs["gamma", "SumInsured", "PremiumPeriod"] = 0.005; +# costs["gamma", "SumInsured", "PremiumFree"] = 0.01; +# costs["gamma_nopremiums", "SumInsured", "PolicyPeriod"] = 0.01; +# +# costs +# +# TestTarif = InsuranceTarif$new(name = "Testtarif", mortalityTable = AVOe2005R.male, type = "annuity", costs=costs) +# q = TestTarif$getTransitionProbabilities(YOB = 1980, age = 30) +# TestTarif = InsuranceTarif$new(name = "Testtarif", mortalityTable = AVOe2005R.male, type = "wholelife", costs=costs) +# TestTarif$getBasicCashFlows(YOB = 1980, age = 30, policyPeriod = 5, deferral = 3, guaranteed=10) +# +# # Gemischte Versicherung, i=1%, AVÖ2005R Unisex, YOB=1980, age=30, Laufzeit=10, Prämienzahlungsdauer=5, +# TestTarif = InsuranceTarif$new(name = "Testtarif", mortalityTable = AVOe2005R.unisex, type = "endowment", costs=costs, i=0.01) +# TestTarif$getBasicCashFlows(YOB = 1980, age = 30, premiumPaymentPeriod = 5, policyPeriod = 10, deferral = 0, guaranteed=0) +# +# TestTarif$costs=costs; +# TestTarif$premiumRefund = 0; +# +# cf = TestTarif$getCashFlows(YOB = 1980, age = 30, premiumPaymentPeriod = 5, policyPeriod = 10, deferral = 0, guaranteed=0); cf +# cfc = TestTarif$getCashFlowsCosts(YOB = 1980, age = 30, premiumPaymentPeriod = 5, policyPeriod = 10, deferral = 0, guaranteed=0); cfc +# +# pv = TestTarif$presentValueCashFlows(cf, age = 30, YOB=1980); pv +# pvc = TestTarif$presentValueCashFlowsCosts(cfc, age=30, YOB=1980); pvc +# +# premiums=TestTarif$premiumCalculation(pv, pvc, premiumSum=15); premiums +# +# +# +# premiums*1000 +# as.array(premiums)*1000 +# +# c("net"=1, "gross"=23, "Zillmer"=44) +# str(as.matrix( premiums)) +# as.matrix(premiums)*1000 +# scf +# cfc +# dim(cfc)[1] +# +# str(cf$premiums_advance) +# calculatePVSurvival(q$q, cf$premiums_advance, cf$premiums_arrears, v=1/1.01) +# calculatePVSurvival(q$q, cf$survival_advance, cf$survival_arrears, v=1/1.01) +# +# calculatePVDeath(q$q, cf$death_SumInsured, v=1/1.01) +# calculatePVDeath(q$q, cf$death_GrossPremium, v=1/1.01) +# calculatePVDeath(q$q, cf$death_PremiumFree, v=1/1.01) +# +# diff --git a/R/ValuationTables.R b/R/ValuationTables.R index 3b32f21..f3b6bf6 100644 --- a/R/ValuationTables.R +++ b/R/ValuationTables.R @@ -4,8 +4,8 @@ library(ggplot2); # (virtual) base class for valuation tables, contains only the name / ID valuationTable=setClass( "valuationTable", - slots=list(name="character", baseYear="numeric", loading="numeric"), - prototype=list(name="Actuarial Valuation Table", baseYear=2000, loading=0), + slots=list(name="character", baseYear="numeric", loading="numeric", modification="function"), + prototype=list(name="Actuarial Valuation Table", baseYear=2000, loading=0, modification=identity), contains="VIRTUAL" ); @@ -106,53 +106,77 @@ setMethod("ages", "valuationTable.joined", ages(object@table1); }) +setGeneric("ageShift", function(object, YOB=1975, ...) standardGeneric("ageShift")); +setMethod("ageShift","valuationTable.ageShift", + function(object, YOB, ...) { + shift = object@ageShifts[toString(YOB),]; + if (is.na(shift)) { + # The row names (YOB) are unfortunately strings, so we cannot easily query them. + # TODO: Change the data.frame to use a real column for the YOB + firstYOB = head(rownames(object@ageShifts), n=1); + lastYOB = tail(rownames(object@ageShifts), n=1); + if (YOB < as.integer(firstYOB)) { + shift = object@ageShifts[firstYOB,]; + } else if (YOB > as.integer(lastYOB)) { + shift = object@ageShifts[lastYOB,]; + } + } + shift + }) setGeneric("deathProbabilities", function(object, ..., YOB=1975) standardGeneric("deathProbabilities")); setMethod("deathProbabilities", "valuationTable.period", function(object, ..., YOB=1975) { - object@deathProbs * (1+object@loading); + object@modification(object@deathProbs * (1+object@loading)); }) setMethod("deathProbabilities","valuationTable.ageShift", function (object, ..., YOB=1975) { qx=object@deathProbs * (1+object@loading); - shift.index=match(YOB, object@shifts, 0); - if (shift.index) {} - # TODO - qx + shift = ageShift(object, YOB); + if (shift>0) { + qx = c(qx[(shift+1):length(qx)], rep(qx[length(qx)], shift)); + } else if (shift<0) { + qx = c(rep(0, -shift), qx[1:(length(qx)-(-shift))]) + } + object@modification(qx) }) + + setMethod("deathProbabilities","valuationTable.trendProjection", function (object, ..., YOB=1975) { -cat("deathProbabilities for valuationTable.trendProjection, YOB=", YOB, "\n") qx=object@deathProbs * (1+object@loading); if (is.null(object@trend2) || length(object@trend2)<=1) { ages=0:(length(qx)-1); damping=sapply(ages, function (age) { object@dampingFunction(YOB+age-object@baseYear) }); # print(data.frame(age=0:(length(qx)-1), trend=object@trend, exponent=-object@trend*damping, damping=damping, baseqx=qx, qx=exp(-object@trend*damping)*qx)[66:90,]); - exp(-object@trend*damping)*qx; + finalqx=exp(-object@trend*damping)*qx; } else { # dampingFunction interpolates between the two trends: weights=sapply(YOB+0:(length(qx)-1), object@dampingFunction); - qx*exp(-(object@trend*(1-weights) + object@trend2*(weights))*(YOB+0:(length(qx)-1)-object@baseYear)) + finalqx=qx*exp(-(object@trend*(1-weights) + object@trend2*(weights))*(YOB+0:(length(qx)-1)-object@baseYear)) } + object@modification(finalqx) }) -# data.frame(x=0:121, qx=deathProbabilities(AVOe2005R.unisex, YOB=1948)); + setMethod("deathProbabilities","valuationTable.improvementFactors", function (object, ..., YOB=1975) { qx=object@deathProbs * (1+object@loading); - (1-object@improvement)^(YOB+0:(length(qx)-1)-object@baseYear)*qx + finalqx=(1-object@improvement)^(YOB+0:(length(qx)-1)-object@baseYear)*qx; + object@modification(finalqx) }) setMethod("deathProbabilities","valuationTable.mixed", function (object, ..., YOB=1975) { qx1=deathProbabilities(object@table1, ..., YOB) * (1+object@loading); qx2=deathProbabilities(object@table2, ..., YOB) * (1+object@loading); - (object@weight1*qx1 + object@weight2*qx2)/(object@weight1 + object@weight2) + mixedqx=(object@weight1*qx1 + object@weight2*qx2)/(object@weight1 + object@weight2); + object@modification(mixedqx) }) setGeneric("periodDeathProbabilities", function(object, ...) standardGeneric("periodDeathProbabilities")); setMethod("periodDeathProbabilities", "valuationTable.period", function(object, ...) { - object@deathProbs * (1+object@loading); + object@modification(object@deathProbs * (1+object@loading)); }) setMethod("periodDeathProbabilities","valuationTable.ageShift", function (object, ..., Period=1975) { @@ -161,7 +185,7 @@ setMethod("periodDeathProbabilities","valuationTable.ageShift", shift.index=match(YOB, object@shifts, 0); if (shift.index) {} # TODO - qx + object@modification(qx) }) setMethod("periodDeathProbabilities","valuationTable.trendProjection", function (object, ..., Period=1975) { @@ -170,25 +194,28 @@ setMethod("periodDeathProbabilities","valuationTable.trendProjection", ages=0:(length(qx)-1); damping=object@dampingFunction(Period-object@baseYear); # print(data.frame(age=0:(length(qx)-1), trend=object@trend, exponent=-object@trend*damping, damping=damping, baseqx=qx, qx=exp(-object@trend*damping)*qx)[66:90,]); - exp(-object@trend*damping)*qx; + finalqx=exp(-object@trend*damping)*qx; } else { # TODO # dampingFunction interpolates between the two trends: weights=sapply(YOB+0:(length(qx)-1), object@dampingFunction); - qx*exp(-(object@trend*(1-weights) + object@trend2*(weights))*(YOB+0:(length(qx)-1)-object@baseYear)) + finalqx=qx*exp(-(object@trend*(1-weights) + object@trend2*(weights))*(YOB+0:(length(qx)-1)-object@baseYear)); } + object@modification(finalqx) }) # data.frame(x=0:121, qx=deathProbabilities(AVOe2005R.unisex, YOB=1948)); setMethod("periodDeathProbabilities","valuationTable.improvementFactors", function (object, ..., Period=1975) { qx=object@deathProbs * (1+object@loading); - (1-object@improvement)^(Period-object@baseYear)*qx + finalqx=(1-object@improvement)^(Period-object@baseYear)*qx; + object@modification(finalqx) }) setMethod("periodDeathProbabilities","valuationTable.mixed", function (object, ..., Period=1975) { qx1=periodDeathProbabilities(object@table1, ..., Period=Period) * (1+object@loading); qx2=periodDeathProbabilities(object@table2, ..., Period=Period) * (1+object@loading); - (object@weight1*qx1 + object@weight2*qx2)/(object@weight1 + object@weight2) + mixedqx=(object@weight1*qx1 + object@weight2*qx2)/(object@weight1 + object@weight2); + object@modification(mixedqx) }) @@ -260,10 +287,10 @@ makeQxDataFrame = function(..., YOB=1972, Period=NA) { names(data) = lapply(data, function(t) t@name); if (missing(Period)) { cat("Year of birth: ", YOB, "\n"); - data = lapply(data, function(t) cbind(x=t@ages, y=deathProbabilities(t, YOB=YOB))) + data = lapply(data, function(t) cbind(x=ages(t), y=deathProbabilities(t, YOB=YOB))) } else { cat("Period: ", Period,"\n"); - data = lapply(data, function(t) cbind(x=t@ages, y=periodDeathProbabilities(t, Period=Period))) + data = lapply(data, function(t) cbind(x=ages(t), y=periodDeathProbabilities(t, Period=Period))) } list.names = names(data) @@ -312,6 +339,7 @@ plotValuationTables = function(data, ..., title = "", legend.position=c(0.9,0.1) } pl# + coord_flip() } + plotValuationTables(mort.AT.census.1869.male, mort.AT.census.1869.female, mort.AT.census.2011.male, mort.AT.census.2011.female, AVOe2005R.male, AVOe2005R.female, YOB=1972,title="Vergleich österreichische Sterbetafeln, YOB=1972 (bei Generationentafeln)") plotValuationTables(mort.AT.census.2001.male, AVOe2005R.male, YOB=1972, title="Vergleich österreichische Sterbetafeln") diff --git a/R/ValuationTables_Austria_Annuities.R b/R/ValuationTables_Austria_Annuities.R index a52c4f0..2a354a2 100644 --- a/R/ValuationTables_Austria_Annuities.R +++ b/R/ValuationTables_Austria_Annuities.R @@ -229,5 +229,6 @@ AVOe2005R.unisex.group.av=AVOe2005R_gen.av("AVÖ 2005R unisex group (age-shifted ############################################################################### +options("scipen" = 3) t=AVOe2005R.male; deathProbabilities(t, YOB=2001) diff --git a/R/ValuationTables_Austria_Census.R b/R/ValuationTables_Austria_Census.R index 84ce4f9..cad3bbc 100644 --- a/R/ValuationTables_Austria_Census.R +++ b/R/ValuationTables_Austria_Census.R @@ -58,9 +58,9 @@ mort.AT.census.1991.female = censtable(a.vz.dataF, name="ÖVSt 1990/92 F", baseY mort.AT.census.2001.female = censtable(a.vz.dataF, name="ÖVSt 2000/02 F", baseYear=2001, qslot="X2000.02"); mort.AT.census.2011.female = censtable(a.vz.dataF, name="ÖVSt 2010/2012 F", baseYear=2011, qslot="X2010.12"); -mort.AT.census.2001.unisex = valuationTable.mixed(table1=mort.AT.census.2001.m, table2=mort.AT.census.2001.f) +mort.AT.census.2001.unisex = valuationTable.mixed(table1=mort.AT.census.2001.male, table2=mort.AT.census.2001.female) -mort.AT.census.ALL.maleA= makeQxDataFrame( +mort.AT.census.ALL.male = makeQxDataFrame( mort.AT.census.1869.male, mort.AT.census.1880.male, mort.AT.census.1890.male, @@ -75,7 +75,7 @@ mort.AT.census.ALL.maleA= makeQxDataFrame( mort.AT.census.2001.male, mort.AT.census.2011.male); -mort.AT.census.ALL.female=makeQxDataFrame( +mort.AT.census.ALL.female = makeQxDataFrame( mort.AT.census.1869.female, mort.AT.census.1880.female, mort.AT.census.1890.female, @@ -94,5 +94,5 @@ rm(a.vz.dataM, a.vz.dataF, censtable) ############################################################################### -plotValuationTables(mort.AT.census.ALL.male, title="Vergleich österreichische SterbeTables, Männer", legend.position=c(1,0)) -plotValuationTables(mort.AT.census.ALL.female, title="Vergleich österreichische SterbeTables, Frauen", legend.position=c(1,0)) +plotValuationTables(mort.AT.census.ALL.male, title="Vergleich österreichische Sterbetafeln, Männer", legend.position=c(1,0)) +plotValuationTables(mort.AT.census.ALL.female, title="Vergleich österreichische Sterbetafeln, Frauen", legend.position=c(1,0)) -- GitLab