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.