Analysis of the Insurance Portfolio with an Embedded Catastrophe Bond in a Case of Uncertain Parameter of the Insurer’s Share

In this paper, a behavior of an insurer’s portfolio, which consists of two layers: a classical risk process and a special financial instrument, which is known as a catastrophe bond, is analyzed. Especially, a probability of a ruin for such a portfolio is estimated using the Monte Carlo simulations. A special attention is given to a problem of an insurer’s share in a whole insurance market, which associates values of the catastrophic losses with values of the claims for the considered insurer. It is also an important source of a systematic risk. Because such a share is often an uncertain parameter, then a fuzzy number is used to model its value. This approach incorporates the experts’ knowledge. Based on the simulations, observed differences between a crisp and a fuzzy case are described in a more detailed way.