Mean-Variance Optimization of Portfolios with Return of Premium Clauses in a DC Pension Plan with Multiple Contributors under Constant Elasticity of Variance Model

Authors: Bright O. Osu, Edikan E. Akpanibah, Chidinma Olunkwa

Abstract:

In this paper, mean-variance optimization of portfolios with the return of premium clauses in a defined contribution (DC) pension plan with multiple contributors under constant elasticity of variance (CEV) model is studied. The return clauses which permit death members to claim their accumulated wealth are considered, the remaining wealth is not equally distributed by the remaining members as in literature. We assume that before investment, the surplus which includes funds of members who died after retirement adds to the total wealth. Next, we consider investments in a risk-free asset and a risky asset to meet up the expected returns of the remaining members and obtain an optimized problem with the help of extended Hamilton Jacobi Bellman equation. We obtained the optimal investment strategies for the two assets and the efficient frontier of the members by using a stochastic optimal control technique. Furthermore, we studied the effect of the various parameters of the optimal investment strategies and the effect of the risk-averse level on the efficient frontier. We observed that the optimal investment strategy is the same as in literature, secondly, we observed that the surplus decreases the proportion of the wealth invested in the risky asset.

Keywords: DC pension fund, Hamilton Jacobi Bellman equation, optimal investment strategies, stochastic optimal control technique, return of premiums clauses, mean-variance utility.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1316869

References:

[1] J. F. Boulier, S. Huang, G. Taillard G. Optimal management under stochastic interest rates: the case of a protected defined contribution pension fund, Insurance 28(2) (2001), 173–189.
[2] P. Battocchio, F. Menoncin. Optimal pension management in a stochastic framework, Insurance 34(1) (2004) 79–95.
[3] J. Gao. Stochastic optimal control of DC pension funds, Insurance, 42(3) (2008), 1159–1164.
[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] Z. Chubing, R. Ximing. Optimal investment strategies for DC pension with a stochastic salary under affine interest rate model. Hindawi Publishing Corporationhttp://dx.doi.org/10.1155/2013/297875, (2013).
[6] 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.
[7] J. Gao. Optimal investment strategy for annuity contracts under the constant elasticity of variance (CEV) model, Insurance, 45(1) (2009), 9–18.
[8] D. Blake, D. Wright, Y. M. Zhang. Target-driven investing: Optimal investment strategies in defined contribution pension plans under loss aversion, Journal of Economic Dynamics and Control 37 (2012), 195-209.
[9] A. J. G. Cairns, D. Blake, K. Dowd, Stochastic lifestyling: optimal dynamic assetallocation for defined contribution pension plans, Journal of Economic Dynamics &Control 30(5) (2006) 843–877.
[10] R. Korn, T. K. Siu, A.Zhang. Asset allocation for a DC pension fund under regime switching environment. European Actuarial Journal 1(2011), 361-377.
[11] J. Gao. Optimal portfolios for DC pension plans under a CEV model, Insurance: Mathematics and Economics 44 (2009), 479-490.
[12] G. Dawei, Z. Jingyi. Optimal investment strategies for defined contribution pension funds with multiple contributors”, http://ssrn.com/abstract=2508109 (2014).
[13] B. O. Osu, E. E. Akpanibah, B I. Oruh. Optimal investment strategies for defined contribution (DC) pension fund with multiple contributors via Legendre transform and dual theory, International journal of pure and applied researches, 2(2) (2017), 97-105.
[14] E. E. Akpanibah, S. K. Samaila. Stochastic strategies for optimal investment in a defined contribution (DC) pension fund, International Journal of Applied Science and Mathematical Theory, 3(3) (2017), 48-55.
[15] L. He, Z. Liang. Optimal investment strategy for the DC plan with the return of premiums clauses in a mean-variance framework, Insurance, 53(2013), 643-649.
[16] D. Sheng, X. Rong. Optimal time consistent investment strategy for a DC pension with the return of premiums clauses and annuity contracts, Hindawi Publishing Corporation vol (2014) http://dx.doi.org/10.1155/2014/862694. 1-13.
[17] D Li, X. Rong, H. Zhao, B. Yi. Equilibrium investment strategy for DC pension plan with default risk and return of premiums clauses under CEV model, Insurance 72(2017), 6-20.
[18] T. Björk, A. Murgoci. A general theory of Markovian time inconsistent stochastic control problems. Working Paper. Stockholm School of Economics http://ssrn.com/abstract=1694759 (2009).
[19] L. He, Z. Liang. Optimal financing and dividend control of the insurance company with proportional reinsurance policy. Insurance: Mathematics & Economics 42(2008), 976–983.
[20] L. He, Z. Liang. Optimal financing and dividend control of the insurance company with fixed and proportional transaction costs. Insurance: Mathematics & Economics 44(2009), 88–94.
[21] Z. Liang, J. Huang. Optimal dividend and investing control of an insurance company with higher solvency constraints. Insurance: Mathematics & Economics 49(2011), 501–511.
[22] Y. Zeng, Z. Li. Optimal time consistent investment and reinsurance policies of mean-variance insurers. Insurance: Mathematics & Economics 49(2011), 145–154.