Simulation-Based Analysis of Penalty Function for Insurance Portfolio with Embedded Catastrophe Bond in Crisp and Imprecise Setups

In this paper, important properties of an insurer’s portfolio, which consists of a catastrophe bond and a reinsurance contract, are numerically analysed. Because of stochastic nature of considered processes, simulations and the Monte Carlo (MC) methods are applied. Special attention is paid to estimation and optimization of an average value of the portfolio and to probability of the insurer’s ruin. Moreover, we assume that the ruin event is related to additional expenses, which are modelled by various penalty functions. In the considered numerical examples, apart from strictly crisp sets of parameters, also fuzzy numbers are used to model the possible penalties, which are related to the ruin event.