Compound poisson disorder problem with general disorder prior density

Official URL: https://dx.doi.org/10.1007/s11009-026-10278-7

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.