Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity

Angelos Dassios and Jiwook Jang

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: We use the Cox process (or a doubly stochastic Poisson process) to model the claim arrival process for catastrophic events. The shot noise process is used for the claim intensity function within the Cox process. The Cox process with shot noise intensity is examined by piecewise deterministic Markov process theory. We apply the model to price stop-loss catastrophe reinsurance contract and catastrophe insurance derivatives. The asymptotic distribution of the claim intensity is used to derive pricing formulae for stop-loss reinsurance contract for catastrophic events and catastrophe insurance derivatives. We assume that there is an absence of arbitrage opportunities in the market to obtain the gross premium for stop-loss reinsurance contract and arbitrage-free prices for insurance derivatives. This can be achieved by using an equivalent martingale probability measure in the pricing models. The Esscher transform is used for this purpose.

JEL-codes: C1 F3 G3 (search for similar items in EconPapers)
Date: 2003-01
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Citations: View citations in EconPapers (76)

Published in Finance and Stochastics, January, 2003, 7(1), pp. 73-95. ISSN: 1432-1122

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