IIARD International Institute of Academic Research and Development

INTERNATIONAL JOURNAL OF APPLIED SCIENCES AND MATHEMATICAL THEORY (IJASMT )

E- ISSN 2489-009X
P- ISSN 2695-1908
VOL. 10 NO. 4 2024
DOI: 10.56201/ijasmt.v10.no4.2024.pg8.20

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Strategized Optimization of Accumulating Pension Wealth Portfolio under the Constant Elasticity of Variance (CEV) Model

K. N. C. Njoku

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Abstract

An optimal Pension investment strategy, under the Constant Elasticity of Variance (CEV) model is developed. The Pension Fund Investor (PFI) invested in both a risky asset (stock) and a riskless asset (Cash account), modeled with CEV process and constant interest rate, respectively. Here, the Pension Fund Administrator (PFA) considered and investigated the relevance/significance of extra stochastic contribution, during non-turbulent period, as a form of extra voluntary contribution, as provided by the Pension Reform Act of 2006, as amended. A constrained Pension Wealth optimization program was developed and transformed into a nonlinear partial differential equation, using the associated Hamilton Jacobi Bellman equation. The explicit solution of the constant relative risk aversion (CRRA) is obtained, using Legendre transform, dual theory, and change of variable methods. I presented and proved theorem on pension wealth investment strategy and the optimal utility function is also presented. It is established herein, with the optimal utility function that the extra stochastic contribution is minimally significant to the satisfaction of the PFI, due to its partial presence in the optimal utility function strategy.

keywords:

Strategized; Portfolio; CRRA; CEV; Accumulating Pension.

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