4 - Classical Risk Model with a Franchise and a Liability Limit

Abstract

In this chapter, we deal with the classical risk model under the additional assumption that an insurance company applies a franchise and a liability limit. To be more precise, we consider three cases: the insurance company establishes a franchise only, a liability limit only and both a franchise and a liability limit. Assuming that claim sizes are exponentially distributed we find analytic expressions for the infinite-horizon survival probabilities in these cases. The expressions turn out different on certain intervals. Moreover, we investigate how a franchise and a liability limit change the survival probability for small and large enough initial surpluses.