Abstract
The increasing number of natural catastrophes leads to severe losses for production, in infrastructure and individual property. Classical insurance mechanisms may not be sufficient in dealing with such losses because of dependencies among sources of losses, huge values of damages, problems with adverse selection and moral hazard. To cope with dramatic consequences of such extreme events integrated policy is required. In this paper we discuss the model of portfolio which consists of a few layers of insurance and financial instruments, like catastrophe fund, catastrophe bonds, governmental help, etc. We use approach based on neutral martingale method and simulations. We price the catastrophe bond applying Vasicek model used for zero-coupon bond under assumption of independence between catastrophe occurrence and behavior of financial market. We discuss the effects of uncertainties which arise from estimation of rare events with serious, catastrophic consequences like natural catastrophes.
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References
Borch, K. (1974). The Mathematical Theory of Insurance. Lexington: Lexington Books.
Buckley, J. J. (2004). Fuzzy Statistics. New York: Springer.
Cox, S. H., Fairchild, J. R., & Pedersen, H. W. (2000). Economic aspects of securitization of risk. ASTIN Bulletin, 30(1), 157–193.
Cummins, J. D., Doherty, N., & Lo, A. (2002). Can insurers pay for the ”big one”? Measuring the capacity of insurance market to respond to catastrophic losses. Journal of Banking and Finance, 26.
D’Arcy, S. P., & France, V. G. (1992). Catastrophe futures: A better hedge for insurers. Journal of Risk and Insurance, 59(4), 575–600.
Ermoliev, Yu. M., Ermolyeva, T.Yu., McDonald, G., Norkin, V. I. (2001). Problems on insurance of catastrophic risks. Cybernetics and Systems Analysis, 37(2).
Ermolieva, T., & Ermoliev, Y. (2005). Catastrophic risk management: flood and seismic risks case studies. In S. W. Wallace, & W. T. Ziemba (Eds.), Applications of Stochastic Programming, MPS-SIAM Series on Optimization. Philadelphia, PA, USA.
Ermolieva, T., Romaniuk, M., Fischer, G., & Makowski, M. (2007). Integrated model-based decision support for management of weather-related agricultural losses. In O. Hryniewicz, J. Studzinski, & Shaker M. Romaniuk (Eds.), Enviromental informatics and systems research. Vol. 1: Plenary and session papers - EnviroInfo 2007. Verlag.
Freeman, P. K., & Kunreuther, H. (1997). Managing Environmental Risk Through Insurance. Boston: Kluwer.
Froot, K. A. (2001). The market for catastrophe risk: A clinical examination. Journal of Financial Economics, 60(2).
George, J. B. (1999). Alternative reinsurance: Using catastrophe bonds and insurance derivatives as a mechanism for increasing capacity in the insurance markets. CPCU Journal.
Harrington, S. E., & Niehaus, G. (2003). Capital, corporate income taxes, and catastrophe insurance. Journal of Financial Intermediation, 12(4).
MacKellar, L., Freeman, P., & Ermolieva, T. (1999). Estimating Natural Catastrophic Risk Exposure and the Benefits of Risk Transfer in Developing Countries. http://www.iiasa.ac.at/Research/CAT/paris.pdf.
Malamud, B. D., & Turcotte, D. L. (2006). The applicability of power-law frequency statistics to floods. Journal of Hydrology, 322.
McGhee, C. (2004). Market Update: The Catastrophe Bond Market at Year-End 2003. Guy Carpenter & Company, Inc. and MMC Security Corporation.
Muermann, A. (2008). Market price of insurance risk implied by catastrophe derivatives. North American Actuarial Journal, 12(3), 221–227.
Niedzielski, J. (1997). USAA places catastrophe bonds. National Underwriter, 16
Nowak, P., Romaniuk, M., & Ermolieva, T. (2008). Integrated management of weather – related agricultural losses – computational approach. In E. Wilimowska, L. Borzemski, A. Grzech, & Wroclaw J. Swiatek (Eds.), Information Systems Architecture and Technology.
Nowak, P., & Romaniuk M. (2009). Portfolio of financial and insurance instruments for losses caused by natural catastrophes. In Z. Wilimowska, L. Borzemski, A. Grzech, Wroclaw J. Swiatek (Eds.), Information Systems Architecture and Technology. IT Technologies in Knowledge Oriented Management Process.
Nowak, P., & Romaniuk, M. (2009). Fuzzy Approach to Evaluation of Portfolio of Financial and Insurance Instruments (to be published)
Nowak, P., & Romaniuk, M. (2010). Computing option price for Levy process with fuzzy parameters. European Journal of Operational Research, 201(1).
O’Brien, T. (1997). Hedging strategies using catastrophe insurance options. Insurance: Mathematics and Economics, 21(2), 153–162.
Pinelli, J.-P., & Gurley, K. R., et al. (2008). Validation of probabilistic model for hurricane insurance loss projections in Florida. Reliability Enigeeniring and System Safety, 93.
Rao, A. R., & Hamed, K. H. (2000). Flood Frequency Analysis. CRC Press.
Romaniuk, M., & Ermolieva, T. (2005). Application EDGE software and simulations for integrated catastrophe management. International Journal of Knowledge and Systems Sciences, 2(2), 1–9.
Skees, J., Varangis, P., Larson, D., & Siegel, P. (2002). Can Financial Markets be Tapped to Help Poor People Cope with Weather Risks? Policy Research Working Paper 2812, The World Bank Development Research Group, Rural Development (March 2002).
Stone, J. M. (1973). A theory of capacity and the insurance of catastrophe risks. The Journal of Risk and Insurance, 40.
Vaugirard, V. E. (2003). Pricing catastrophe bonds by an arbitrage approach. The Quarterly Review of Economics and Finance, 43, 119–132.
Walker, G. (1997). Current developments in catastrophe modelling. In N.R. Britton, & J. Olliver (Eds.), Financial Risks Management for Natural Catastrophes. Brisbane, Australia: Griffith University.
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Nowak, P., Romaniuk, M., Ermolieva, T. (2012). Evaluation of Portfolio of Financial and Insurance Instruments: Simulation of Uncertainty. In: Ermoliev, Y., Makowski, M., Marti, K. (eds) Managing Safety of Heterogeneous Systems. Lecture Notes in Economics and Mathematical Systems, vol 658. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22884-1_17
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DOI: https://doi.org/10.1007/978-3-642-22884-1_17
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