On the Investment Strategy, Effect of Inflation and Impact of Hedging on Pension Wealth during Accumulation and Distribution Phases

Bright O Osu,K N C Njoku K N C Njoku,B I Oruh B I Oruh

doi:10.46481/jnsps.2020.62

Abstract

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.

Highlights

Introduction nerableThis is true because at old age, they are mentally, eco-One of the major challenges that old people are faced with is economic insecurity
Considering the dual relationship between pension wealth, it follows that the optimal strategy will appreciate frictionless, which is unrealistic
There exists a modifying factor which depends on time, only, just like in [13] and this modifying factor controls investment decision of the PPM

Summary

Materials and Methods

For maximization of the expected utility of the terminal wealth became necessary. The Constant Relative Risk Aversion (CRRA) utility function, and (or) the Constant Absolute Risk Aversion (CARA) utility function were used to maximize where t is the time, r is the short interest rate andy is the wealth. [9] used the CRRA and the CARA to maximize terminal wealth, and this triggered our and the optimal strategy u∗ = u∗s such that research. With a stochastic salary, under the affine interest rate model was constructed. In this work, they introduced the notion of ” Relative Pension Wealth”, that is, where a pension plan member only considers his/her post-retirement benefit, the ratio of the pension wealth to his terminal salary. They introduced the notion of ” Relative Pension Wealth”, that is, where a pension plan member only considers his/her post-retirement benefit, the ratio of the pension wealth to his terminal salary. [9] considered a mini-

Legendre Transformation

Model Assumption

Sensitivity Analysis and

Discussion

Conclusion