On the Modified Optimal Investment Strategy for Annuity Contracts under the Constant Elasticity of Variance (CEV) Model

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.