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.
Österreichische Systematik der Wissenschaftszweige (ÖFOS)
- 101014 Numerische Mathematik
- 401117 Weinbau
- 101024 Wahrscheinlichkeitstheorie
- 101007 Finanzmathematik