Optimal premium allocation under stop-loss insurance using exposure curves

Abstract

Determining the retention level in the stop-loss insurance risk premium for both insurer and reinsurer is an important factor in pricing. This paper aims to set optimal reinsurance with respect to the joint behavior of the insurer and the reinsurer under stop-loss contracts. The dependence between the costs of insurer and reinsurer is expressed as a function of retention ($d$) and maximum-cap ($m$) levels. Based on the maximum degree of correlation, the optimal levels for $d$ and $m$ are derived under certain claim distributions (Pareto, Gamma and Inverse Gamma). Accordingly, the risk premium and exposure curves for both parties are based on the selected distributions. Quantification of the premium share over derived exposure curves based on the optimized retention and maximum levels and the maximum loss risk is obtained using VaR and CVaR as risk measures.

Keywords

• Stop-Loss reinsurance
• Optimal Retention
• Optimal Cap
• Premium Share
• Exposure Curves
• Risk Measures

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