In this paper we solve the basic fractional analogue of the classical linear-quadratic Gaussian regulator problem in continuous-time with partial observation. For a controlled linear system where both the state and observation processes are driven by fractional Brownian motions, we describe explicitly the optimal control policy which minimizes a quadratic performance criterion. Actually, we show that a separation principle holds, i.e., the optimal control separates into two stages based on optimal filtering of the unobservable state and optimal control of the filtered state. Both finite and infinite time horizon problems are investigated.

Haberman and Sung (1994) have presented a dynamic model for a defined benefit occupational pension scheme which considered two types of risk: the “contribution rate” and the “solvency” risk. The current paper, extends this work by deriving optimal funding control procedures for determining the contribution rate for the case of a stochastic model with incomplete state information, making use of the separation principle. The stochastic inputs modelled are the investment returns and the benefit outgo.