Property Claim Services by Compound Poisson Process And Inhomogeneous Levy Process

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Muhammed A. S. Murad

Abstract

In this paper, stochastic compound Poisson process is employed to value the catastrophic insurance options and model the claim arrival process for catastrophic events, which were written in the loss period , during which the catastrophe took place. Here, a time compound process gives the underlying loss index before and after  whose losses are revaluated by inhomogeneous exponential Levy process factor. For this paper, an exponential Levy process is used to evaluate the well-known European call option in order to price Property Claim Services catastrophe insurance based on catastrophe index.


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References

Aase, K. (1999). An Equilibrium Model of Catastrophe Insurance Futures and Spreads. Geneva Papers on Risk and Insurance Theory 24, 69-96.
Biagini, F., Bregman, Y., and Meyer-Brandis, T (2009). Pricing of catastrophe insurance options written on a loss index with re-estimation.
Chistensen, C.V., and Schmidli, H. (2000) Pricing catastrophe insurance products based on actually reported claims, Insurance: Mathematics and economic 27.
Chang, Carolyn W, Chang, Jack S and Yu, Min-Teh. (1996). Pricing Catastrophe Insurance Futures Call Spreads: A Randomized Operational Time Approach. The Journl of Risk and Insurance, Vol. 63, No. 4, 599-617.
Dalang, R.C., Morton, A., and Willinger, W. Equivalent Martingale Measures and No-Arbitrage in Stochastic SecuritiesMarket Models. Stochastics and Stochastic Reports 29 (1990):185-201.
Delbaen, F., and Haezendonck, J. A Martingale Approach to Premium Calculation Principles in an Arbitrage Free Market. Insurance: Mathematics and Economics 8 (1989): 269-77.
Gerber, Hans U. and Elias S.W. Shiu. (1994). Option pricing by Esscher Transforms, Transactions of the Society of Actuaries, Vol. XLVI.
Gerber, Hans U. and Elias S.W. Shiu. (1995) Martingale Approach to Pricing Perpetual American Options, Proceedings of the 4th AFIR International Colloquium, Orlando, April 20-22, vol. 2.
Hogg, R.V., and Craig, A.T. (1995). Introduction to mathematical statistic, Prentice Hall, Fifth edition.
Muerman, A. (2000). Pricing catastrophe insurance derivatives, Discussion paper 400, financial markets group and the Wharton School.
Murad. Muhammad Amin. S. (2017). Esscher Transform and Equivalent Martingale in Pricing Derivative Securities. Cihan International Journal of Social Science, 1(1), 37-44.
Schradin, H.R. (1996). PCS Catastrophe Insurance Options-A new Instrument for managing catastrophe risks, The 6th AFIR international Colloquium, Nuremberg.