We propose a model for an insurance loss index and the claims process of a single insurance company holding a fraction of the total number of contracts that captures both ordinary losses and losses due to catastrophes. In this model we price a catastrophe derivative by the method of utility indifference pricing. The associated stochastic optimization problem is treated by techniques for piecewise deterministic Markov processes. A numerical study illustrates our results.
Keywords: Catastrophe derivatives; Insurance mathematics; Modeling catastrophe losses; Piecewise deterministic Markov process; Utility indifference pricing.