Partially Observed Non-linear Risk-sensitive Optimal Stopping Control for Non-linear Discrete-time Systems

摘要

In this paper we introduce and solve the partially observed optimal stoppingudnon-linear risk-sensitive stochastic control problem for discrete-time non-linearudsystems. The presented results are closely related to udprevious results for finiteudhorizon partially observed risk-sensitive stochastic control problem. Anudinformation state approach is used and a new (three-way) separation principle establishedudthat leads to a forward dynamic programming equation and a backward uddynamic programming inequality equation (both infinite dimensional). udA verification theorem is udgiven that establishes the optimal control and optimal stopping time. udThe risk-neutral optimaludstopping stochastic control problem is also discussed.