Effect of Supplementary Premium on the Optimal Portfolio Policy in a Defined Contribution Pension Scheme with Refund of Premium Clauses
In this paper, we studied the effect of supplementary premium on the optimal portfolio policy in a defined contribution (DC) pension scheme with refund of premium clauses. This refund clause allows death members’ next of kin to withdraw their relative’s accumulated wealth during the accumulation period. The supplementary premium is to help sustain the scheme and is assumed to be stochastic. We considered cases when the remaining wealth is equally distributed and when it is not equally distributed among the remaining members. Next, we considered investments in cash and equity to help increase the remaining accumulated funds to meet up with the retirement needs of the remaining members and composed the problem as a continuous time mean-variance stochastic optimal control problem using the actuarial symbol and established an optimization problem from the extended Hamilton Jacobi Bellman equations. The optimal portfolio policy, the corresponding optimal fund size for the two assets and also the efficient frontier of the pension members for the two cases was obtained. Furthermore, the numerical simulations of the optimal portfolio policies with time were presented and the effect of the supplementary premium on the optimal portfolio policy was discussed and observed that the supplementary premium decreases the optimal portfolio policy of the risky asset (equity). Secondly we observed a disparity between the optimal policies for the two cases.
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 A. J. G. Cairns, D. Blake, K. Dowd. Stochastic life styling: optimal dynamic assetallocation for defined contribution pension plans, Journal of Economic Dynamics &Control 30(5) (2006) 843–877.
 M. Giacinto, F. Gozzi, S. Federico, 2011. Pension funds with a minimum guarantee: a stochastic control approach. Finance and Stochastic. 15, 297-342
 J. Gao. Stochastic optimal control of DC pension funds, Insurance, 42(3) (2008), 1159–1164.
 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.
 P. Battocchio, F. Menoncin. Optimal pension management in a stochastic framework, Insurance34(1) (2004) 79–95.
 Njoku, K.N. C. Osu, B. O, Akpanibah, E. E. and Ujumadu, R. N. (2017) ‘Effect ofExtraContribution on Stochastic Optimal Investment Strategies for DC Pension with Stochastic Salary under the Affine Interest Rate Model’ Journal of Mathematical Finance, 7, 821-833.
 E. E. Akpanibah, and O. Okwigbedi (2018) ‘’ Optimal Portfolio Selection in a DC Pension withMultiple Contributors and the Impact of Stochastic Additional Voluntary Contribution on the Optimal Investment Strategy’’ International journal of mathematical and computational sciences, 12(1) (2018), 14-19.
 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.
 J. Gao. Optimal portfolios for DC pension plans under a CEV model, Insurance: Mathematics and Economics 44 (2009), 479-490.
 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.
 L. He, Z. Liang. The optimal investment strategy for the DC plan with the return of premiums clauses in a mean-variance framework, Insurance, 53(2013), 643-649.
 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
 B. O. Osu, E. E. Akpanibah, O. Olunkwa. 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, 12(5) (2018), 85-90.
 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
 E. E. Akpanibah, B. O. Osu. Optimal Portfolio Selection for a Defined Contribution Pension Fund with Return Clauses of Premium with Predetermined Interest Rate under Mean-variance Utility, Asian Journal of Mathematical Sciences 2(2).(2018) 19-29
 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
 Y. Zeng, Z. Li. Optimal time consistent investment and reinsurance policies for mean-variance insurers. Insurance: Mathematics & Economics 49(2011), 145–154.
 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.
 Z. Liang, J. Huang. Optimal dividend and investing control of an insurance company with higher solvency constraints. Insurance: Mathematics & Economics 49(2011), 501–511.
 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).