util: Calculate utility of total consumption and bequest
In sstoeckl/pensionfinanceLi: Optimal Pension Decisions in Liechtenstein

Description Usage Arguments Value Examples

Expected Utility for total cash-flows is calculated here and used for optimization

util(
  ret_age,
  tw3,
  c,
  c2,
  nu2,
  nu3,
  ra,
  delta,
  alpha,
  beta,
  c_age,
  gender,
  gender_mortalityTable,
  w0,
  CF,
  li,
  lg,
  c1,
  s1,
  s2,
  s3,
  w2,
  rho2,
  rho3,
  ret,
  retr,
  psi,
  verbose = FALSE,
  warnings = TRUE
)

`ret_age`	Decision Variable: retirement age, can be set anywhere between 60 and 70 (default: 65)
`tw3`	Decision Variable: third pillar portfolio allocation (given either as vector or as matrix with entries) for all years. HERE: Choose only allocation to stocks, bonds and real estate, cash will be determined as fraction missing to sum up to one
`c`	Decision Variable: fraction of income that is consumed while still working (current assumption: constant)
`c2`	Decision Variable: second pillar savings as fraction of gross income (still missing: health, a-fonds-perdu payments)
`nu2`	Decision Variable: fraction of second pillar savings that is converted to life-long pension
`nu3`	Decision Variable: fraction of third pillar savings that is converted to life-long pension
`ra`	Given variable: Risk Aversion of Agent
`delta`	Given Variable: Time Preference
`alpha`	Decision Variable: parameter to choose fraction of wealth NOT consumed during retirement but kept for investment (and subsequent consumption) - see file 'Consumption_3p.ods'
`beta`	Given variable: Relative Weight of bequest utility
`c_age`	Given variable: the investor's current age (assuming birthday is calculation-day)
`gender`	Given variable: gender, 0=male and 1=female
`gender_mortalityTable`	Given variable: MortalityTable to use for gender 0=male and 1=female, e.g. 'baseTable(AVOe2005R.male)'
`w0`	Given variable: time c_age wealth that is not disposable, assumption: still available at retirement (no growth or decline), alternatively: expected wealth (that is not disposable) at retirement, stays the same over time
`CF`	Given Variables: income shocks, such as inheritance (not currrently imlemented)
`li`	Given variable: gross labor income at time 0 (in the last year before birthday)
`lg`	Given variable: labor growth rate (in real terms, constant)
`c1`	Given variable: first pillar savings as fraction of gross income
`s1`	Given variable: vector consisting of two components: c(number of contribution years at age=c_age,historical average yearly income until c_age)
`s2`	Given variable: savings in second pillar as of t=0
`s3`	Given variable: liquid wealth - invested in the third pillar (current assumption: no tax advantage for third pillar)
`w2`	Given variable: portfolio allocation in second pillar (assumed to be fixed and not influenced by the decision maker)
`rho2`	Given variable: conversion factor in second pillar for regular retirement age
`rho3`	Given variable: conversion factor in third pillar for regular retirement age
`ret`	Given variable: investment return scenarios (nominal)
`retr`	Given variable: investment return scenarios (real)
`psi`	Given variable: spread to take a loan/leverage for third pillar savings
`verbose`	optional: show additional information while calculating utility (default: FALSE)
`warnings`	optional: should warnings be given? (default=TRUE)

Expected utility

data(ret); data(retr)
MortalityTables::mortalityTables.load("Austria_Annuities")

util_ex <- util(ret_age=65,c_age=42,
                tw3=c(.25,.25,.25),
                c=0.6,c2=.12,nu2=.5,nu3=0.01,ra=4,delta=0.02,alpha=0.96,beta=0.75,gender=0,
                gender_mortalityTable=MortalityTables::baseTable(AVOe2005R.male),
                w0=300000,CF=NULL,li=100000,lg=0.01,c1=0.07,s1=c(15,80000),s2=300000,s3=300000,
                w2=setNames(c(.30,.30,.30,.10,0),c("msci","b10","recom","libor","infl")),
                rho2=0.05,rho3=0.04,ret=ret,retr=retr,psi=0.015)
util_ex2 <- util(ret_age=65,c_age=64,
                tw3=setNames(c(1,0,0),c("msci","b10","recom")),
                c=1,c2=0,nu2=0,nu3=0,ra=0,delta=0,alpha=1,beta=0,gender=0,
                gender_mortalityTable=MortalityTables::baseTable(AVOe2005R.male),
                w0=0,CF=NULL,li=0,lg=0,c1=0,s1=c(0,0),s2=0,s3=0,
                w2=setNames(c(0,0,0,1,0),c("msci","b10","recom","libor","infl")),
                rho2=0.0001,rho3=0.0001,ret=ret[,,1:10],retr=retr[,,1:10],psi=0)