Expected optimal feedback with time-varying parameters

In this paper we derive the closed loop form of the Expected Optimal Feedback rule, sometimes called passive learning stochastic control, with time varying parameters. As such this paper extends the work of Kendrick (Stochastic control for economic models, 1981; Stochastic control for economic models, 2002, Chap. 6) where parameters are assumed to vary randomly around a known constant mean. Furthermore, we show that the cautionary myopic rule in Beck and Wieland (J Econ Dyn Control 26:1359–1377, 2002) model, a test bed for comparing various stochastic optimizations approaches, can be cast into this framework and can be treated as a special case of this solution.