Ruin probabilities of a surplus process described by PDMPs
The class of risk processes described by a piecewise deterministic Markov process is considered, i.e. between claim arrivals epochs the process follows a deterministic path described by a measurable continuously differentiable function. An integro-differential equation for the ultimate ruin probability for the surplus process is derived. Under a certain assumption, it is transformed into the ruin probability of a risk process whose premiums depend on the current reserves. Then the ruin probability and its upper bounds are obtained using change of the probability measure and local adjustment coefficients. The example is considered when the claim-size is exponentially distributed.
scientific article; zbMATH DE number 5278778