A Solvency II Partial Internal Model Considering Reinsurance and Counterparty Default Risk

Estimating the expected capital and its variability is a crucial objective for a non-life insurance company, which enables the firm to develop effective management strategies. Many studies have been devoted to this topic, with simulative approaches being especially employed for solving the complexity of the interacting risks, not manageable through closed-form solutions. In this paper, we present a realistic framework based on Solvency II for the definition of next-year capital of a non-life insurer, including reinsurance treaties and counterparty default risk, in a multi-line of business setting. We determine the mean and variance of the stochastic capital considering both quota share and excess-of-loss reinsurance. We show how these closed-form results enable the analysis of many different real-world strategies, granting the insurer the possibility of choosing the optimal policy without the computational resources and time constraints required by simulative approaches.