Abstract
In this work, the optimal pension wealth investment strategy during the decumulation phase, in a defined contribution (DC) pension scheme is constructed. The pension plan member is allowed to invest in a risk free and a risky asset, under the constant elasticity of variance (CEV) model. The explicit solution of the constant relative risk aversion (CRRA) and constant absolute risk aversion (CARA) utility functions are obtained, using Legendre transform, dual theory, and change of variable methods. It is established herein that the elastic parameter, β, say, must not necessarily be equal to one (β ≠ 1). A theorem is constructed and proved on the wealth investment strategy. Observations and significant results are made and obtained, respectively in the comparison of our various utility functions and some previous results in literature.
Highlights
There are two major designs of pension plan, namely, the defined benefit (DB) pension, and the defined contribution (DC) pension plan
The pension plan member is allowed to invest in a risk free and a risky asset, under the constant elasticity of variance (CEV) model
In the DC pension plan, the contributions are defined, the retirement benefits depends on the contributions and the investment returns, and the contributors bears the financial risk
Summary
There are two major designs of pension plan, namely, the defined benefit (DB) pension, and the defined contribution (DC) pension plan. In that of the DB, the benefits of the plan member are defined, and the sponsor bears the financial risk. In the DC pension plan, the contributions are defined, the retirement benefits depends on the contributions and the investment returns, and the contributors (the plan members) bears the financial risk. Cairns et al [4] did a work on, “stochastic life styling: optimal dynamic asset allocation for defined contribution pension plans. Mwanakatwe et al [14] analysed the optimal investment strategies for a DC pension fund under the Hull-White interest rate model. In order to deal with optimal investment strategy, the need for maximization of the expected utility of the terminal wealth became necessary.
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