Optimal stopping for partially observed piecewise-deterministic Markov processes

This paper deals with the optimal stopping problem under partial observation for piecewise-deterministic Markov processes. We first obtain a recursive formulation of the optimal filter process and derive the dynamic programming equation of the partially observed optimal stopping problem. Then, we propose a numerical method, based on the quantization of the discrete-time filter process and the inter-jump times, to approximate the value function and to compute an actual $\epsilon$-optimal stopping time. We prove the convergence of the algorithms and bound the rates of convergence

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

In this paper we introduce and solve the partially observed optimal stopping non-linear risk-sensitive stochastic control problem for discrete-time non-linear systems. The presented results are closely related to previous results for finite horizon partially observed risk-sensitive stochastic control problem. An information state approach is used and a new (three-way) separation principle established that leads to a forward dynamic programming equation and a backward dynamic programming inequality equation (both infinite dimensional). A verification theorem is given that establishes the optimal control and optimal stopping time. The risk-neutral optimal stopping stochastic control problem is also discussed

Controlled diffusion processes

This article gives an overview of the developments in controlled diffusion processes, emphasizing key results regarding existence of optimal controls and their characterization via dynamic programming for a variety of cost criteria and structural assumptions. Stochastic maximum principle and control under partial observations (equivalently, control of nonlinear filters) are also discussed. Several other related topics are briefly sketched.Comment: Published at http://dx.doi.org/10.1214/154957805100000131 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org