Stochastic model of a pension plan

TL;DR

This paper develops a stochastic model for pension plans, analyzing stock market assumptions, comparing investment strategies, and estimating pension fund dynamics and survival probabilities using historical data.

Contribution

It introduces a stochastic framework for pension modeling, validating assumptions with real data, and assesses the effectiveness of different investment strategies.

Findings

Stock market index reflects company profits accurately.

No advantage in wholly owning a super trust for pension funds.

Stock earnings follow an exponential Brownian motion with estimated parameters.

Abstract

Structuring a viable pension plan is a problem that arises in the study of financial contracts pricing and bears special importance these days. Deterministic pension models often rely on projections that are based on several assumptions concerning the "average" long-time behavior of the stock market. Our aim here is to examine some of the popular "average" assumptions in a more realistic setting of a stochastic model. Thus, we examine the contention that investment in the stock market is similar to gambling in a casino, while purchasing companies, after due diligence, is safer under the premise that acting as a holding company that wholly owns other companies avoids some of the stock market risks. We show that the stock market index faithfully reflects its companies' profits at the time of their publication. We compare the shifted historical dynamics of the S\&P500's aggregated financial earnings to its value, and find a high degree of correlation. We conclude that there is no benefit to a pension fund in wholly owning a super trust. We verify, by examining historical data, that stock earnings follow an exponential (geometric) Brownian motion and estimate its parameters. The robustness of this model is examined by an estimate of a pensioner's accumulated assets over a saving period. We also estimate the survival probability and mean survival time of the accumulated individual fund with pension consumption over the residual life of the pensioner.