Catastrophe Insurance

Pricing Catastrophe Insurance Derivatives

We investigate the valuation of catastrophe insurance derivatives that are traded at the Chicago Board of Trade. By modeling the underlying index as a compound Poisson process we give a representation of no-arbitrage price processes using Fourier analysis. This characterization enables us to derive the inverse Fourier transform of prices in closed form for every fixed equivalent martingale meas...

Catastrophe Insurance and Optimal Investment

In the insurance market, the insurers who provide catastrophe insurance face with the risk of rare, but huge catastrophe claims. The introduction of catastrophe related securities into the marketplace provide the insurers the instruments to hedge some of the catastrophe risks they are facing. A catastrophe related security is tied to the prespecified catastrophe claims, while independent to oth...

Catastrophe Insurance and the Demand for Deductibles

Utility indifference pricing of insurance catastrophe derivatives

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 piecewi...

Catastrophe Insurance Modeled by Shot-Noise Processes

Shot-noise processes generalize compound Poisson processes in the following way: a jump (the shot) is followed by a decline (noise). This constitutes a useful model for insurance claims in many circumstances; claims due to natural disasters or self-exciting processes exhibit similar features. We give a general account of shot-noise processes with time-inhomogeneous drivers inspired by recent re...