In this paper, optimal investment strategies for defined contribution (DC) Pension, with extra contribution are studied. Our model permits the plan member to make a defined extra contribution, as provided in the Nigerian Pension Reform Act of 2004. The plan member is free to invest in risk-free asset, and in two risky assets. A stochastic differential equation of the pension wealth that takes into account certain agreed proportions of the plan member's salary, paid as contribution, and extra contribution towards the pension fund, is presented. The Hamilton-Jacobi-Bellman (H-J-B) equation, Legend transformation, and Dual theory are used to obtain the explicit solution of the optimal investment strategies for constant relative risk aversion (CRRA) utility function. We observed that the plan member will increase the proportion of his wealth to be invested in bond and stock and will reduce the proportion to be invested in cash.

This work investigates the effect of Inflation and the impact of hedging on the optimal investment strategies for a prospective investor in a DC pension scheme, using inflation-indexed bond and inflation-linked stock. The model used here permits the plan member to make a defined contribution, as provided in the Nigerian Pension Reform Act of 2004. The pension plan member is allowed to invest in risk-free asset (cash), and two risky assets (i.e., the inflation-indexed bond and inflation-linked stock). A stochastic differential equation of the pension wealth that takes into account certain agreed proportions of the plan member’s salary, paid as contribution towards the pension fund, is constructed and presented. The Hamilton-Jacobi-Bellman (H-J-B) equation, Legendre transformation, and dual theory are used to obtain the explicit solution of the optimal investment strategies for CRRA utility function. Our investigation reveals that the inflation have significant negative effect on wealth investment strategies, particularly, the RRA(w) is not constant with the investment strategy, since the inflation parameters and coefficient of CRRA utility function have insignificant input on the investment strategies, and also the inflation-indexed bond and inflation-linked stock has a positive damping effect (hedging) on the severe effect of inflation.

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.

In this paper, we seek to investigate the effect of inflation on the optimal investment strategies for DC Pension. Our model permits the plan member to make a defined contribution, as provided in the Nigerian Pension Reform Act of 2004. The plan member is free to invest in risk-free asset and two risky assets. A stochastic differential equation of the pension wealth that takes into account certainly agreed proportions of the plan member's salary, paid as a contribution towards the pension fund, is presented. The Hamilton-Jacobi-Bellman (H-J-B) equation, Legendre transformation, and dual theory are used to obtain the explicit solution of the optimal investment strategies for CRRA utility function. Our investigation reveals that the inflation has significant negative effect on optimal investment strategy, particularly, the CCRA is not constant with the investment strategy since the inflation parameters and coefficient of CRRA utility function have insignificant input on the investment strategy.

This paper studies the various results obtained in literature on the investment strategy, the effect of inflation and impact ofh edging on the Pension Wealth generation. The explicit solution of the constant relative risk aversion (CRRA) and constant absolute risk aversion (CARA) utility functions are obtained, both in the accumulation and distribution phase, using Legendre transform, dual theory, and change of variable techniques. It is established herein that the elastic parameter (beta) is not equal to one (beta neq 1), based on the assumption of our model. Theorems are constructed and proved on the various wealth investment strategies. Observations and significant results are made and obtained, respectively in the comparison of our various utility functions and some previous results in literature. Sensitivity analysis and Simulations on the various utility functions and optimal strategies during the accumulation and distribution phase are presented; when the existence of a elastic parameter that is not equal to one, when there is existence of modifying factors, when there is need for diversification of investment, when there is no significant effect of the choice of risk aversion strategy on investment returns during inflation period, when there is hedging ability of Inflation indexed Bond and Inflation-linked Stock and when there is insignificant effect of the orthogonal relationship between stock and time and nonpayment of pension benefits on the satisfaction of the investors.