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<p>In the literature, Bayesian compound Poisson disorder problem has been solved for only some very special change-time prior distributions. Here we show that the problem with an arbitrary prior density can always be reformulated as a two-dimensional optimal stopping problem for some suitable Markov sufficient statistic. In the two-dimensional state-space, the optimal stopping and continuation regions are separated by a boundary curve. Concrete numerical examples illustrate that this generalized formulation and solution approaches will widen the realistic applications of the compound Poisson disorder problem.</p>

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Compound Poisson Disorder Problem with General Disorder Prior Density

  • 期刊论文

  • 发表日期：

    2026年4月30日

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  • Deniz Sahin,
  • Savas Dayanik,
  • Semih O. Sezer

摘要

In the literature, Bayesian compound Poisson disorder problem has been solved for only some very special change-time prior distributions. Here we show that the problem with an arbitrary prior density can always be reformulated as a two-dimensional optimal stopping problem for some suitable Markov sufficient statistic. In the two-dimensional state-space, the optimal stopping and continuation regions are separated by a boundary curve. Concrete numerical examples illustrate that this generalized formulation and solution approaches will widen the realistic applications of the compound Poisson disorder problem.