Multiple disorder problems for Wiener and compound Poisson processes with exponential jumps
- Gapeev, Pavel
2010 Mathematics Subject Classification
- 60G40 62M20 34K10 62C10 60J60 60J75
- Multiple disorder problem, Wiener process, compound Poisson process, optimal switching, coupled optimal stopping problem, (integro-differential) coupled free-boundary problem, smooth and continuous fit, Itô-Tanaka-Meyer formula
The multiple disorder problem consists of finding a sequence of stopping times 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 exponential jumps. The method of proof is based on reducing the initial optimal switching problems to the corresponding coupled optimal stopping problems and solving the equivalent coupled free-boundary problems by means of the smooth- and continuous-fit conditions.