A generalization of Gerber’s inequality for ruin probabilities in risk-switching models

Abstract

In this paper, we investigate a risk-switching Sparre Andersen model which generalizes several discrete time- as well as continuous time risk models. A Markov chain is used as a ‘switch’ under the assumption that jumps change the amount and/or respective wait time distributions of claims while the insurer can adapt the premiums in response. A generalized Gerber-type inequality for the vector of ruin probabilities is proven showing that the risk-switching models allow sophisticated mathematical results in spite of their complexity.