Optimal non-proportional reinsurance under VaR: the cedant point of view

Abstract

This paper describes the main characteristics of reinsurance distinguishing between facultative and obligatory arrangements and analysing proportional and non-proportional forms thereof. Assuming that both the cedant and the reinsurer are obliged to pay more for larger losses and that the premium principle has to satisfy three basic axioms, it is shown that the limited stop-loss reinsurance is always optimal under VaR risk measure. Furthermore, an empirical analysis is provided for different distributions of the loss random variable.