Abstract
One of the major problems faced in the management of pension funds and plan is how to allocate and control the future flow of contribution likewise the proportion of portfolio value and investments in risky assets. In this work, optimal investment for a stochastic model of a Defined contribution (DC) is investigated such that the model design is analysed yielding an optimized expected utility of the members’ terminal wealth. An optimized solution is derived using the Hamilton Jacobi equation in solving the problem of investment strategy formulated by Constant absolute risk aversion (CARA). However, to consider the changes that occur in the dimension of optimal solutions in optimization problems, mostly, the optimal behaviour of parameters, the sensitivity analysis is considered. Thus, the analysis of the model is carried out herein by utilising the approach of the sensitivity analysis of parameters. This is carried out by using Maple software and varying the values of some model parameters such that the behaviour of each parameter relating to the pension funds invested in the risky assets is determined. The results are presented graphically and using tables thus discussed such that pension investors and stakeholders are advised.
 Keywords: Stochastic; DC Pension funds; Sensitivity analysis; Hamilton-Jacobi-Bellman equation; Optimal investment
Highlights
The management of pension funds has transformed in the recent years from DB pension systems where the employer alone used to contribute to defined contributory pension schemes where both the employer and the employee must contribute a given percentage towards the fund
defined contribution (DC) pension schemes are merged into one pension plan to study the impact of the voluntary contributions on the pension fund invested in the risky asset
The case where the terminal utility is a function of pension purchased at retirement in a stochastic interest-rate environment is been considered in this work
Summary
The management of pension funds has transformed in the recent years from DB pension systems where the employer alone used to contribute to defined contributory pension schemes where both the employer and the employee must contribute a given percentage towards the fund. Defined contribution problems typically deal with the case where the terminal utility is a function of the fund size at retirement.
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