Partially observed optimal stopping problem for discrete-time Markov processes

TL;DR

This paper introduces a new numerical method using optimal quantization to approximate the optimal stopping problem for partially observed discrete-time Markov chains, providing explicit error bounds.

Contribution

It develops a two-step discretization approach combining state space quantization and filter approximation for better numerical solutions.

Findings

Provides explicit error bounds for the approximation

Develops a fully computable method for the value function

Enhances numerical accuracy in partial observation scenarios

Abstract

This paper is dedicated to the investigation of a new numerical method to approximate the optimal stopping problem for a discrete-time continuous state space Markov chain under partial observations. It is based on a two-step discretization procedure based on optimal quantization. First,we discretize the state space of the unobserved variable by quantizing an underlying reference measure. Then we jointly discretize the resulting approximate filter and the observation process. We obtain a fully computable approximation of the value function with explicit error bounds for its convergence towards the true value fonction.