An integrated framework for indicator-based decision analysis in proportional-XL reinsurance

Abstract

This paper investigates the problem of optimal reinsurance by evaluating four critical criteria: ruin probability, variance of retained risk, profit, and expected utility. The study focuses on proportional-XL reinsurance, which combines the benefits of both proportional and excess of loss (XL) reinsurance.

Using a classical risk model with a compound Poisson process for aggregate claims, the paper demonstrates that De Vylder’s approximation effectively estimates the ruin probability from the perspectives of both the insurer and the reinsurer, incorporating a two-dimensional risk process. The impact of reinsurance levels on each criterion is analyzed separately for the insurer and the reinsurer, providing a comprehensive understanding of reinsurance effects.

The optimal reinsurance level is determined by balancing conflicting objectives: maximizing profit and expected utility while minimizing ruin probability and variance. Multiple-criteria decision-making (MCDM) techniques, specifically the COPRAS and COPRAS-G methods, are applied to tailor optimal reinsurance strategies for both parties.

A detailed application of these methods for exponential and Pareto claim distributions enables a comparison based on the portfolio’s tail behavior. The cost-effectiveness of reinsurance agreements is evaluated, showing that reinsurance is more cost-effective than no reinsurance in both models. As expected, the cost-effectiveness of the proposed methods varies depending on the characteristics of the exponential and Pareto distributions.