A Discretization Procedure in Finite Horizon Optimal Stopping Tested on AR(1) Processes

Abstract

A discretization procedure for finite horizon optimal stopping problems in discrete time is developed. This procedure was designed to work well for a large class of discrete time stochastic processes, for which it finds stopping strategies. We test how well the procedure works for AR(1) processes, because we can numerically approximate the value functions associated with stopping this process, so that we can compare these with the results of the discretization procedure. Another reason for looking at AR(1) processes is that these are often used in modelling the price of electricity in demand-side management and this research was started in the context of an investigation of stochastic optimization problems in demand-side management. We aim to provide empirical evidence showing that the discretization procedure is consistent. Properties of the value function of the stopping problem are also derived.