Optimal Stopping of a Risk Process with Disruption and Interest Rates

Abstract

It is a standard approach in classical risk theory to assume a claim process which does not change throughout the whole observation period. Most commonly, encountered models deal with compound Poisson processes. It would be beneficial to investigate more general classes of claim processes with arbitrary distributions of random variables governing inter-occurrence times between losses and loss severities. Further generalization of such framework would be a model allowing for disruptions i.e. changes of such distributions according to some unobservable random variables, representing fluctuating environmental conditions. The question of providing the company with tools allowing for detection of such change and maximizing the returns leads to an optimal stopping problem which we solve explicitly to some extent. Moreover, we provide references to previously examined models as well as numerical examples emphasizing the efficiency of the suggested method.