Numerical method for optimal stopping of hybrid processes

We propose a numerical method to approximate the value function for the optimal stopping problem of a general class of hybrid processes, namely piecewise deterministic Markov processes (PDMP's). Our approach is based on quantization of the post jump location -inter-arrival time Markov chain naturally embedded in the PDMP, and path-adapted time discretization grids. It allows us to derive bounds for the convergence rate of the algorithm and to provide a computable e-optimal stopping time.