Relative Reinsurance Retention Levels

The problem of determining optimal retention levels for a non-life portfolio consisting of a number of independent sub-portfolios was first discussed by de Finetti. He considered retention levels as optimal if they minimized the variance of the insurer's profit from the portfolio subject to the constraint of a fixed level of expected profit. In this paper we consider a similar problem, changing the criterion for optimality to minimizing the probability of ruin, either in discrete or continuous time. We investigate this problem through a series of case studies based on a real portfolio. Keywords: Reinsurance; optimal retention levels; finite time ruin; translated gamma process.