Efficient reinsurance strategies considering counterparty default risk

Insurance companies pursue the objective of increasing their technical profit, but in doing so, they expose themselves to more risks, increasing the variability of their result. In order to balance the potential profitability deriving from the underwriting activity with the related risks, insurers typically resort to reinsurance treaties. In this context arises the problem of finding the optimal treaty which jointly satisfies multiple objectives, typically represented by risk and return metrics. The classical approaches consider only the characteristics of the treaty, neglecting the ones of the reinsurance provider. However, this approach could lead to sub-optimal choices, since it does not consider counterparty default risk. The purpose of this thesis is threefold. Firstly, we extend classical formulas of technical profit of an insurance company to a partial internal model of Solvency II, including the potential default of the reinsurance counterparty. Secondly, we develop a stochastic simulation approach that includes counterparty default risk and potentially other features, for estimating the efficient frontier of reinsurance strategies for a non-life insurance company. Finally, we propose the application of a neural network model for finding the efficient frontier in a multi-objective optimization problem, requiring limited observations and preserving the possibility of deriving the strategies which generate the Pareto front. Numerical applications are performed assuming a multi-line non-life insurer with parameters from the Italian market. The results show the importance of the rating of reinsurers, i.e. counterparty default risk, for the assessment of the optimal reinsurance strategies. Moreover, we show how this risk could become an opportunity in case the reinsurer with high risk offers a discounted price that more than compensate the potential default effect. Finally, the neural network model offers another perspective for determining optimal reinsurance strategies, which can be especially useful in case of high number of potential combinations defining each strategy.