Utility indifference pricing of insurance catastrophe derivatives. (English) Zbl 1405.91256
Summary: 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.
MSC:
| 91B30 | Risk theory, insurance (MSC2010) |
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 91B16 | Utility theory |
| 93E20 | Optimal stochastic control |
| 60J28 | Applications of continuous-time Markov processes on discrete state spaces |
Keywords:
insurance mathematics; catastrophe derivatives; utility indifference pricing; modeling catastrophe losses; piecewise deterministic Markov processReferences:
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