Effect of Inflation on Stochastic Optimal Investment Strategies for DC Pension under the Affine Interest Rate Model

Abstract

In this paper, we seek to investigate the effect of inflation on the optimal investment strategiesfor DC Pension. Our model permits the plan member to make a defined contribution, asprovided in the Nigerian Pension Reform Act of 2004. The plan member is free to invest inrisk-free asset and two risky assets. A stochastic differential equation of the pension wealththat takes into account certainly agreed proportions of the plan member’s salary, paid as acontribution 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 solutionof the optimal investment strategies for CRRA utility function. Our investigation revealsthat the inflation has significant negative effect on optimal investment strategy, particularly,the CCRA is not constant with the investment strategy since the inflation parameters andcoefficient of CRRA utility function have insignificant input on the investment strategy.