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

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  • Pavel Gapeev

Abstract

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.

Suggested Citation

  • Pavel Gapeev, 2006. "Multiple Disorder Problems for Wiener and Compound Poisson Processes With Exponential Jumps," SFB 649 Discussion Papers SFB649DP2006-074, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2006-074
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    References listed on IDEAS

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    1. Alexander Yushkevich, 2001. "Optimal switching problem for countable Markov chains: average reward criterion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(1), pages 1-24, April.
    2. Gapeev, Pavel V., 2005. "The disorder problem for compound Poisson processes with exponential jumps," LSE Research Online Documents on Economics 3219, London School of Economics and Political Science, LSE Library.
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