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

Year 2019, Volume: 2 Issue: 1, 91 - 100, 17.06.2019

Kevin N. C. Njoku Bright O. Osu

https://doi.org/10.33401/fujma.409748

Cited By: 1

Abstract

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.

Keywords

Hamilton-Jacobi Bellman equation, Affine interest rate, Defined contribution pension, Inflation Stochastic optimal control

References

• [1] A. J. G. Cairns, D. Blake, K. Dowd, Stochastic lifestyling: optimal dynamic asset allocation for defined contribution pension plans, J. Econom. Dynam. Control, 30(5) (2006), pp. 843–877.
• [2] J. Gao, Stochastic optimal control of DC pension funds, Insurance, 42(3) (2008), 1159–1164.
• [3] J. F. Boulier, S. Huang, G. Taillard, Optimal management under stochastic interest rates: the case of a protected defined contribution pension fund, Insurance, 28(2) (2001), 173–189.
• [4] G. Deelstra, M. Grasselli, P. F. Koehl, Optimal investment strategies in the presence of a minimum guarantee, Insurance, 33(1) (2003), 189–207.
• [5] J. Xiao, Z. Hong, C. Qin, The constant elasticity of variance(CEV) model and the Legendre transform-dual solution for annuity contracts, Insurance, 40(2) (2007), 302–310.
• [6] J. Gao, Optimal portfolios for DC pension plans under a CEV model, Insurance Math. Econom., 44 (2009), 479-490,
• [7] C. Zhang, X. Rong, R. Ximing, Optimal investment strategies for DC pension with stochastic salary under affine interest rate model, Discrete Dyn. Nat. Soc., (2013), Article ID 297875, 11 pages, http://dx.doi.org/10.1155/2013/297875
• [8] B. Othusitse, X. Xiaoping, Stochastic Optimal Investment under Inflamatory Market with Minimum Guarantee for DC Pension Plans, J. Math., 7(3) (2015).
• [9] O. Vasicek, An equilibrium characterization of the term structure, J. Math Finance, 5(2) (1977), 177–188.
• [10] J. C. Cox, J. E. Ingersoll, S. A. Ross, A theory of the term structure of interest rates, Econometrica, 53(2) (1985), 385–407.
• [11] D. Duffie, R. Kan, A yield-factor model of interest rates, Math. Finance, 6(4) (1996), 379–406.
• [12] M. Jonsson, R. Sircar, Optimal investment problems and volatility homogenization approximations, in Modern Methods, in Scientific Computing and Applications, 75 of ATO Science Series II, Springer, Berlin, Germany, 2002, pp. 255–281
• [13] P. Battocchio, F. Menoncin, Optimal pension management in a stochastic framework, Insurance, 34(1) (2004), 79–95.
• [14] J. Gao, Optimal investment strategy for annuity contracts under the constant elasticity of variance (CEV) model, Insurance, 45(1) (2009), 9–18.
• [15] H. Nan-Wei, H. Mao-Wei, Optimal asset allocation for DC pension plans under inflation, Insurance Math. Econom., 51 (2012), 172-181.