Multiple Disorder Problems for Wiener and Compound Poisson Processes With Exponential Jumps

Abstract

The multiple disorder problem consists of finding a sequence of stoppingtimes which are as close as possible to the (unknown) times of ``disorder´´when the distribution of an observed process changes its probability characteristics.We present a formulation and solution of the multiple disorder problem for a Wiener and a compound Poisson process with exponentialjumps. The method of proof is based on reducing the initial optimalswitching problems to the corresponding coupled optimal stopping problemsand solving the equivalent coupled free-boundary problems by meansof the smooth- and continuous-fit conditions.