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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
