Abstract
In this paper, we propose an approach to explore reinsurance optimization for a non-life multi-line insurer through a simulation model that combines alternative reinsurance treaties. Based on the Solvency II framework, the model maximises both solvency ratio and portfolio performance under user-defined constraints. Data visualisation helps understanding the numerical results and, together with the concept of the Pareto frontier, supports the selection of the optimal reinsurance program. We show in the case study that the methodology can be easily restructured to deal with multi-objective optimization, and, finally, the selected programs from each proposed problem are compared.
Highlights
The recent introduction of new risk-based reporting and solvency frameworks is encouraging non-life insurers to focus much more than previously on risk, value, and capital management of their portfolios
Prompted by the recent insurance regulatory developments aiming at the harmonisation of risk assessment procedures, considerable attention has turned to embedding value at risk (VaR) and tail value at risk (TVaR) risk measures in the study of optimal reinsurance models
To have a more complete view of the impacts in terms of risk mitigation, we focus on combination the solvency position m that maximizes the sooflvtheneciynsruartiaoncsert(cmom) =pasncyrutb(tmy )s .eTarhcehidnegnofomrinthaetor considers the premium risk solvency capital requirement derived by a partial internal model and it is computed as: scrt(m) = VaR99.5% Stn+1(m) − Stn+1(m) where we apply a VaR evaluated at 99.5% confidence level as prescribed by the Solvency II directive [28]
Summary
The recent introduction of new risk-based reporting and solvency frameworks is encouraging non-life insurers to focus much more than previously on risk, value, and capital management of their portfolios. The authors obtain an optimal share of premiums and liability transfers in order to minimize the total amount of the technical provisions and minimum capital requirement, based on the methodology provided by Quantitative Impact Study 5 In this case, we differ from this approach because our aim is to provide a multi-objective optimization framework that considers both risk and return. It is defined as the difference between the amount of premiums paid to the reinsurance company bri,t+1 and the aggregate claim amount paid by the reinsurer Xir,t+1 plus the commissions Cir,t+1 paid by the reinsurer in proportional treaties Given this framework, our aim is to select the optimal combination m∗ for the insurance company by considering the effects on both the profitability and the risk. These alternative problems will be analysed in the numerical part
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