On the Investment Approach in a DC Pension Scheme for Default Fund Phase IV under the Constant Elasticity of Variance (CEV) Model -by Kevin. N. C Njoku, Bright. O. Osu and Philip U. Uzom

# On the Investment Approach in a DC Pension Scheme for Default Fund Phase IV under the Constant Elasticity of Variance (CEV) Model-by Kevin. N. C Njoku, Bright. O. Osu and Philip U. Uzom

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) is obtained, using Legendre transform, dual theory, and change of variable methods. It is established herein, with a proposition that the elastic parameter, $\beta$, say, must not necessarily be equal to one $(\beta\neq1)$. A theorem is constructed and proved on the wealth investment strategy. Through a sensitivity analysis, we exposed the dangers of CRRA utility options during the period after retirement.

Keywords: Annuity contracts; CRRA; CARA; DC; CEV; FUND DEFAULT.