DC Pension Plan with Refund of Contributions under Affine Interest Rate Model

Main Article Content

Udeme O. Ini
Obinichi C. Mandah
Edikan E. Akpanibah

Abstract

This paper studies the optimal investment plan for a pension scheme with refund of contributions, stochastic salary and affine interest rate model. A modified model which allows for refund of contributions to death members’ families is considered. In this model, the fund managers invest in a risk free (treasury) and two risky assets (stock and zero coupon bond) such that the price of the risky assets are modelled by geometric Brownian motions and the risk free interest rate is of affine structure. Using the game theoretic approach, an extended Hamilton Jacobi Bellman (HJB) equation which is a system of non linear PDE is established. Furthermore, the extended HJB equation is then solved by change of variable and variable separation technique to obtain explicit solutions of the optimal investment plan for the three assets using mean variance utility function. Finally, theoretical analyses of the impact of some sensitive parameters on the optimal investment plan are presented.

Keywords:
Pension scheme, extended HJB equation, investment plan, refund clause, stochastic salary, affine interest rate.

Article Details

How to Cite
Ini, U. O., Mandah, O. C., & Akpanibah, E. E. (2020). DC Pension Plan with Refund of Contributions under Affine Interest Rate Model. Asian Journal of Probability and Statistics, 7(2), 1-16. https://doi.org/10.9734/ajpas/2020/v7i230175
Section
Original Research Article

References

He L, Liang Z. The optimal investment strategy for the DC plan with the return of premiums clauses in a mean-variance framework, Insurance. 2013;53:643-649.

Sheng D, Rong X. Optimal time consistent investment strategy for a DC pension with the return of premiums clauses and annuity contracts, Hindawi Publishing Corporation; 2014.
Available:http://dx.doi.org/10.1155/2014/862694 1-13

Osu BO, Akpanibah EE, Olunkwa O. Mean-variance optimization of portfolios with return of premium clauses in a DC pension plan with multiple contributors under constant elasticity of variance model. International Journal of Mathematical and Computational Sciences Pure and Applied Researches. 2018;12(5):85-90.

Li D, Rong X, Zhao H, Yi B. Equilibrium investment strategy for DC pension plan with default risk and return of premiums clauses under CEV model. Insurance. 2017;72:6-20.

Wang Y, Fan S, Chang H. DC pension plan with the return of premium clauses under inflation risk and volatility risk. J. Sys. Sci. & Math. Scis. 2018;38(4):423-437.

Akpanibah EE, Ini UO. Portfolio selection strategies with return clause in a DC pension fund. Asian Research Journal of Mathematics. 2019;15(3):1–15.

Akpanibah EE, Osu BO, Ihedioha SA. On the optimal asset allocation strategy for a defined contribution pension system with refund clause of premium with predetermined interest under Heston’s volatility model. J. Nonlinear Sci. Appl. 2020;13(1):53–64.

Cairns AJG, Blake D, Dowd K. Stochastic life styling: Optimal dynamic asset allocation for defined contribution pension plans. Journal of Economic Dynamics & Control. 2006;30(5):843–877.

Battocchio P, Menoncin F. Optimal pension management in a stochastic framework. Insurance. 2004; 34(1):79–95.

Gao J. Stochastic optimal control of DC pension funds. Insurance. 2008;42(3):1159–1164.

Deelstra G, Grasselli M, Koehl PF. Optimal investment strategies in the presence of a minimum guarantee. Insurance. 2003;33(1):189–207.

Zhang C, Rong X. Optimal investment strategies for DC pension with astochastic salary under affine interest rate model. Hindawi Publishing Corporation; 2013.
Available:http://dx.doi.org/10.1155/2013/297875.

Akpanibah EE, Osu BO, Njoku KNC, Akak EO. Optimization of wealth investment strategies for a DC pension fund with stochastic salary and extra contributions. International Journal of Partial Diff. Equations and Application. 2017;5(1):33-41.

Duffie D, Kan R. A yield-factor model of interest rates. Mathematical Finance. 1996;6(4):379–406.

Björk T, Murgoci A. A general theory of Markovian time inconsistent stochastic control problems. Working Paper. Stockholm School of Economics; 2010.
Available:http://ssrn.com/abstract=1694759

He L, Liang Z. Optimal financing and dividend control of the insurance company with fixed and proportional transaction costs. Insurance: Mathematics & Economics. 2009;44:88–94.

Liang Z, Huang J. Optimal dividend and investing control of an insurance company with higher solvency constraints. Insurance: Mathematics & Economics. 2011;49:501–511.

Zeng Y, Li Z. Optimal time consistent investment and reinsurance policies for mean-variance insurers. Insurance: Mathematics & Economics. 2011;49:145–154.