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Model_Master.R
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Model_Master.R
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# Actuarial Valuation in a simple setting
# Yimeng Yin
# 5/27/2015
# This program consists of following files:
# Model_master.R
# Model_Decrements.R
# Model_Import_Plan.R
# Model_InvReturns.R
# Model_Population.R
# Model_IndvLiab.R
# Model_AggLiab.R
# Model_Sim.R
# Functions.R
# Data:
# Package "pp.prototypes"
# Package "decrements"
# winklevossdata.rdata: generated by "Inputs_import_Decrements.R" using "Data/Winklevoss(6).xlsx" and "Data/GAM-1971-Male.xls".
# example_Salary_benefit.RData: generated by "Inputs_Salary_Benefit.R" using "Data/PA-PERS.xlsx". ((no longer used in curretn version)
# Goals:
# 1. Conduct actuarial valuations each year during a time period of 100 years, allowing for stochastic investment returns.
# 2. Conduct the stochastic simulation for 2000 times.
# Assumptions
# Plan Desgin
# Beneficiary: : Retirement Only; No disability, death, surivorship benefits
# Benfit formula: % of FAS per YOS; FAS for last # years
# Retirment age : NO early retirement
# Vesting: : Vested if YOS > #
# Cost Method
# 1) EAN(Entry Age Normal)
# 2) PUC(Projected Unit Credit)
# Actuarial Assumptions
# Decrements: Mortality, termination, disability
# Salary scale
# Assumed interest rate
# Inflation
# Productivity
# Contribution rules:
# 1. Sponsor contributes full ADC, which equals the amount of plan cost(Normal cost + supplemental cost) in all periods.
# 2. Sponsor contributes ADC with a cap, which equals a percentage of total payroll.
# 3. Sponsor contributes a fixed percentage of payroll.
# Outputs
# Actuarial liability
# Normal costs
# Assets
# UAAL
# Funded Ratio
## List of tasks:
# How to deal with negative asset values and contributions
# How to set parameter g in constant percent amortization method. Now infl + prod
print(paramlist$runname)
#*********************************************************************************************************
# 0. Parameters (deprecated) ####
#*********************************************************************************************************
if(devMode) source("Dev_Params.R") else {
# Define Other parameters that depend on the fundamental parameters just imported.
paramlist$range_age <- with(Global_paramlist, min.age:max.age)
paramlist$range_ea <- c(Global_paramlist$min.age:(paramlist$r.max - 1))
paramlist$v <- with(paramlist, 1/(1 + i)) # discount factor, just for convenience
}
#*********************************************************************************************************
# 1.1 Importing Decrement tables and Calculating Probabilities ####
#*********************************************************************************************************
source("Model_Decrements.R")
# Output: Decrement (data.frame)
#*********************************************************************************************************
# 1.2 Import Salary table and initial retirement benefit table ####
#*********************************************************************************************************
## Inputs
# Data frames:
# - data frame for initial actives
# - data frame for initial retirees
# - data frame for salary scale
# Parameters:
# - planname: plan to be selected from the data frames above. From the RunControl file
# - paramList
# Notes:
# 1. User must provide the following data frames
# "salary": a complete salary table containing salary history of current actives and projected salary path for future workers,
# both of which are calculated based on a salary table of current actives from the AV and assumptions on salary growth.
# "benefit": a data frame containing average retirement benefit payment(including both service retirement and deferred retirement)
# of all valid ea and age combos.
# 2. Note that avgben is only used to calculate the current and projected values of benefits and liabilities of retirees at year 1. Future retirees'
# benefits and liabilities are calculated based on their salary history provided in "salary".
# 3. I don't think in "avgben" we need average benefit for all combos of ea and age. All we need is actually average benefits
# by age. Once we have that we can assign an arbitrary ea to it an throw it into the model. Note that the AV of NJ-TPAF only contains
# average benefits for retirees and vested terms by age group. Also note that if service retirees and vested terms follow the same mortality table
# and have the same COLA rule, I don't think we need to distinguish between them.
source("Model_Import_Plan.R")
#*********************************************************************************************************
# 1.3 Actual investment return. ####
#*********************************************************************************************************
source("Model_InvReturns.R")
#*********************************************************************************************************
# 2. Population ####
#*********************************************************************************************************
source("Model_Population.R")
gc()
#*********************************************************************************************************
# 3. Individual actuarial liabilities, normal costs and benenfits ####
#*********************************************************************************************************
source("Model_IndivLiab.R")
gc()
#*********************************************************************************************************
# 4. Aggregate actuarial liabilities, normal costs and benenfits ####
#*********************************************************************************************************
source("Model_AggLiab.R")
gc()
#*********************************************************************************************************
# 5. Simulation ####
#*********************************************************************************************************
source("Model_Sim.R")
#*********************************************************************************************************
# 6. Results ####
#*********************************************************************************************************
options(digits = 4, scipen = 6)
# select variables to be displayed in the kable function. See below for a list of all avaiable variables and explanations.
var.display <- c("year", "AL", "AA", "FR", "NC", "SC", "UAAL",
"AL.act_PR", "AL.ret_PR","AL.term_PR", "AL.Ben_PR",
"NC.act_PR", "NC.term_PR", "MA_PR",
#"AL_PR", "NC_PR", "SC_PR", "C_PR", "ERC_PR",
# "PR", "PR.growth",
# "ExF",
# "UAAL", "EUAAL", "LG", "NC", "SC",
#"ADC", "EEC", "ERC",
"C", "B", "B.v", "B.v_B", "B_PR"
# "I.r" , "I.e"
# "i", "i.r"
#, "dERC_PR"
# "AM", "PR",
# "C_ADC"
)
r1 <- penSim_results %>% mutate(B.v_B = B.v / B * 100) %>% filter(sim == 2, year %in% 1:105) %>% select(one_of(var.display))
kable(r1, digits = 3)
# Running time of major modules
Time_liab # liability
Time_wf # workforce
Time_prep_loop # Preparing for the loop
Time_loop # the big loop
(Time_liab + Time_wf + Time_prep_loop + Time_loop)[3]/60 # # of minutes
# AL: Total Actuarial liability, which includes liabilities for active workers and pensioners.
# NC: Normal Cost
# MA: Market value of assets.
# AA: Actuarial value of assets.
# EAA:Expected actuarial value of assets.(used with asset smoothing method in TPAF)
# UAAL: Unfunded accrued actuarial liability, defined as AL - NC
# EUAAL:Expected UAAL.
# PR: payroll
# LG: Loss/Gain, total loss(positive) or gain(negative), Caculated as LG(t+1) = (UAAL(t) + NC(t))(1+i) - C - Ic - UAAL(t+1),
# AM: Amount to be amortized at period t, it is the sum of loss/gain and shortfall in ADC payment.
# i is assumed interest rate. AMs of each period will be amortized seperately.
# SC: Supplement cost
# ADC: ADC
# C : Actual contribution
# C_ADC: shortfall in paying ADC (C - ADC). Note that negative number means shortall.
# B : Total benefit payment(currently all to retirees)
# Ic: Assumed interest from contribution, equal to i*C if C is made at the beginning of time period. i.r is real rate of return.
# Ia: Assumed interest from AA, equal to i*AA if the entire asset is investible.
# Ib: Assumed interest loss due to benefit payment, equal to i*B if the payment is made at the beginning of period
# I.r : Total ACTUAL interet gain, I = i.r*(AA + C - B), if AA is all investible, C and B are made at the beginning of period.
# Funded Ratio: AA / AL
# C_PR: contribution as % of payroll
#*********************************************************************************************************
# 6. Writing outputs ####
#*********************************************************************************************************
outputs_list <- list(paramlist = paramlist,
Global_paramlist = Global_paramlist,
decrement = decrement,
results = penSim_results,
ind_active = AggLiab$ind_active,
ind_retiree = AggLiab$ind_retiree,
ind_term = AggLiab$ind_term,
demo_summary= pop$demo_summary,
#liab = if(paramlist$save.liab) liab else "Not saved",
#demo = if(paramlist$save.demo) pop else "Not saved",
entrant_dist = entrants_dist)
# Save outputs to specified folder
if(!file.exists(folder_run)) dir.create(folder_run)
# filename_outputs <- paste0("Outputs_", paramlist$runname, "_" , format(Sys.Date(), "%m-%d-%Y"), ".RData")
filename_outputs <- paste0("Outputs_", paramlist$runname, ".RData")
save(outputs_list, file = paste0(folder_run,"/", filename_outputs))
gc()