Optimality of Reinsurance Treaties under a Mean - Ruin Probability Criterion

Abstract

The minimization of the probability of ruin is a crucial criterion for determining the effect of the form of reinsurance on the wealth of the cedant and is a very important factor in choosing optimal reinsurance. However, this optimization criterion alone does not generally lead to a rational decision for an optimal choice of reinsurance. This criterion acts only on the risk (minimizing it via the probability of ruin), but it does not affect the technical benefit. That is to say, the insurer should not choose the optimal reinsurance treaty if it is not beneficial. We propose a new reinsurance optimization strategy that maximizes the technical benefit of an insurance company while maintaining a minimal level for the probability of ruin. The objective is to optimize reinsurance with efficiency and ease of computation, using Genetic algorithms.

Improved Estimator of the Conditional Tail Expectation in the case of heavy-tailed losses

“…The application of these alternative measures has gained interest growing in literature and industry. In particular, the CT E, due to its properties and its effectiveness in different fields such as finance and actuaries, its use and studies keep increasing (see, e.g., [15], [34], [18], [16] and references therein). In the literature, the estimation of the CT E and its asymptotic normality under the assumption that the second moment of the loss variable is finite has been established but this assumption is very restrictive in practical problems.…”