Stochastic Optimal Investment under Inflationary Market with Minimum Guarantee for DC Pension Plans

  •  Othusitse Basimanebotlhe    
  •  Xiaoping Xue    


The paper studies the optimal investment strategies to
partake in a defined contribution (DC) pension fund, with the expected minimum guarantee process. The pension fund manager aspires to maximize the surplus, where his benefit lies in a complete market that is subjected to inflation rate. There are only three assets of investment being; the non risky asset and two risky assets. The dynamics of the wealth in our model
takes into account a certain proportion of the client's
salary paid as the contribution towards the pension fund and any other extra amount paid to amortize the fund.

Applying the method of stochastic optimal control to the portfolio management problem, a non-linear second order differential equation for the value function was derived. A constant risk relative aversion (CRRA) utility function was considered to obtain the explicit solutions for the optimal investment strategies. Finally, a numerical simulation is presented to illustrate the behaviour of the model.

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