Stochastic control of a pension fund model with first‐order Markov‐dependent parameters

Abstract

The well known problem of the optimal control of a stochastic discrete linear system with independent parameters and with a quadratic objective functional is generalized to the case where the parameters of the system constitute a first-order Markov chain. The solution to this more general problem is obtained by the principles of stochastic dynamic programming, and the ‘bi-feedback’ nature of the optimal controls is explained. The results are applied to the solution of a 25-period stochastic pension funding problem where it is assumed that the market returns constitute a first-order Markov chain.