An Investment Model for a DC Pension System with Refund Clause under Quadratic Utility - Njoku * , K.N.C. (International Journal of Mathematical Analysis and Modelling, 2024)
Following the Nigerian pension reform act of 2004, there is a clause mandating the pension fund administrators (PFAs) in the defined contributory pension scheme to make a refund to their retirement savings account (RSA) holder’s family who died during the accumulation phase. As good as this clause is to RSA holders; it posed a serious challenge to PFAs on the investment strategy to be used under this condition. In this paper, the optimal investment strategy (OIS) is studied for defined contributory pension with return of premium clause under quadratic utility function. The charge on balance by pension fund administrators and the mortality risk of members of the scheme during the accumulation period by introducing return of premium clause is considered. To achieve this, a portfolio consisting of a risk free and a risky asset with charge on balance by pension fund administrators is considered and the Abraham De Moivre force function is used to establish the mortality rate of members during accumulation. Furthermore, we obtained an optimization problem using dynamic programming approach. Using Legendre transformation and Dual theory, the value function, OIS with return clause is obtained under quadratic utility function. Finally, numerical simulations of the effect of some sensitive parameters on the OIS were obtained and analyzed.