On optimal investment strategy of pension funds with a minimum guarantee under Knightian uncertainty

A continuous-time stochastic control model of optimal management was proposed for a defined contribution pension fund with a minimum guarantee. A pension fund managers utility was characterized from the fund wealth on an infinite horizon by α-maxmin expected utility (α-MEU), by which he differentiates ambiguity and ambiguity attitude under Knightian uncertainty. Pension fund managers value function was derived by the stochastic control theory. The explicit expressions for both the optimal allocation strategy in feedback form and the value function which is a solution to the HJB equation were obtained.