Ruin theory with risk proportional to the free reserve and securitization

A model is proposed for addressing investment risk of the free reserve, in the form of credit or currency risk. This risk is expressed by a constant factor α that represents the recovery rate of a bond or a devaluation factor. Securitization (e.g. with a CAT-bond like product) yields a constant amount K upon such an event. The model equation is an integro-differential equation with deviating arguments. We compute the analytical solution for the probability of survival and also show results of simulations using quasi-Monte Carlo methods.