Optimal Portfolio Selection in a DC Pension with Multiple Contributors and the Impact of Stochastic Additional Voluntary Contribution on the Optimal Investment Strategy

Authors: Edikan E. Akpanibah, Okwigbedi Oghen’Oro

Abstract:

In this paper, we studied the optimal portfolio selection in a defined contribution (DC) pension scheme with multiple contributors under constant elasticity of variance (CEV) model and the impact of stochastic additional voluntary contribution on the investment strategies. We assume that the voluntary contributions are stochastic and also consider investments in a risk free asset and a risky asset to increase the expected returns of the contributing members. We derived a stochastic differential equation which consists of the members’ monthly contributions and the invested fund and obtained an optimized problem with the help of Hamilton Jacobi Bellman equation. Furthermore, we find an explicit solution for the optimal investment strategy with stochastic voluntary contribution using power transformation and change of variables method and the corresponding optimal fund size was obtained. We discussed the impact of the voluntary contribution on the optimal investment strategy with numerical simulations and observed that the voluntary contribution reduces the optimal investment strategy of the risky asset.

Keywords: DC pension fund, Hamilton-Jacobi-Bellman, optimal investment strategies, power transformation method, stochastic, voluntary contribution.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1316468

References:

[1] J. Gao, Optimal investment strategy for annuity contracts under the constant elasticity of variance (CEV) model, Insurance, 45(1) (2009), 9–18.
[2] N. Dokuchaev, X. Yu Zhou, “Optimal investment strategies with bounded risks, general utilities, and goal achieving,” Journal of Mathematical Economics, vol.35, no.2, pp.289–309, 2001
[3] B. Othusitse, X. Xiaoping, Stochastic Optimal Investment under Inflammatory Market with Minimum Guarantee for DC Pension Plans, Journal of Mathematics, 7(3) (2015).
[4] K.N. CNjoku., B. O. Osu., E. E. Akpanibah, R. N. Ujumadu. Effect of Extra Contribution on Stochastic Optimal Investment Strategies for DC Pension with Stochastic Salary under the Affine Interest Rate Model. Journal of Mathematical Finance, 7, (2017) 821-833.
[5] M. Jonsson, R. Sircar. Optimal investment problems and Volatility homogenization approximations, in Modern Methods in Scientific Computing and Applications, 75(2002), 255-281, Springer, Berlin, Germany
[6] B.O. Osu, E. E. Akpanibah, K.N.C Njoku,. On the Effect of Stochastic Extra Contribution on Optimal Investment Strategies for Stochastic Salary under the Affine Interest Rate Model in a DC pension Fund. General Letters in Mathematic, Vol. 2, No. 3, 2017, 138-149
[7] G. Deelstra, M. Grasselli, P. F. Koehl, Optimal investment strategies in the presence of a minimum guarantee, Insurance, 33(1) (2003), 189–207.
[8] 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.
[9] A. J. G. Cairns, D. Blake, K. Dowd, Stochastic lifestyling: optimal dynamic asset allocation for defined contribution pension plans, Journal of Economic Dynamics &Control 30(5) (2006) 843–877
[10] J. Gao, Stochastic optimal control of DC pension funds, Insurance, 42(3) (2008), 1159–1164.
[11] 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.
[12] 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.
[13] Z. Chubing, R. Ximing, Optimal investment strategies for DC pension with stochastic salary under affine interest rate model. Hindawi Publishing Corporationhttp://dx.doi.org/10.1155/2013/297875, (2013).
[14] G. Dawei, Z. Jingyi, Optimal investment strategies for defined contribution pension funds with multiple contributors”, http://ssrn.com/abstract=2508109 (2014).
[15] P. Battocchio, F. Menoncin, Optimal pension management in a stochastic framework, Insurance 34(1) (2004) 79–95.
[16] 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.
[17] R. Abade, Pension Reforms Act 2004: What’s in it for You? www.Newage-online.com (2004).