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Market Consistent Pricing of Insurance Products

Published online by Cambridge University Press:  17 April 2015

Semyon Malamud
Affiliation:
ETH Zurich, Department of Mathematics, CH-8092 Zurich, Switzerland
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Abstract

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We present the first step in a program to develop a comprehensive, unified equilibrium theory of asset and liability pricing. We give a mathematical framework for pricing insurance products in a multiperiod financial market. This framework reflects classical economic principles (like utility maximization) and generates pricing algorithms for non-hedgeable insurance risks.

Type
Articles
Copyright
Copyright © ASTIN Bulletin 2008

Footnotes

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ETH Zurich, Department of Mathematics, CH-8092 Zurich, Switzerland.

References

[1] Barrieu, P. and El Karoui, N. (2007) Pricing, hedging and optimal designing derivatives via minimization of risk measures. To appear in: Volume on Indifference Pricing, Carmona, R. (Ed.), Princeton University Press.Google Scholar
[2] Bühlmann, H., Delbaen, F., Embrechts, P. and Shiryaev, A.N. (1998) On the Esscher transform in discrete finance models, Astin Bulletin 28, 171186.CrossRefGoogle Scholar
[3] Cochrane, J.H. (2001) Asset Pricing. Princeton University Press, Princeton and Oxford.Google Scholar
[4] Davis, M.H.A. (1998) Option pricing in incomplete markets . In: Mathematics of Derivative Securities, Dempster, M.A.H. and Pliska, S.R. (Eds.), Cambridge University Press.Google Scholar
[5] De Finetti, B. (1957) Su un’impostazion alternativa dell teoria collectiva dell richio. Transactions of the XVth international congress of Actuaries 2, 433443.Google Scholar
[6] De Jong, F. (2005) Valuation of pension liabilities in incomplete markets . Preprint, DNB Working Paper 67, December 2005, Netherlands.Google Scholar
[7] Delbaen, F., Grandits, P., Rheinlander, T., Samperi, D., Schweizer, M. and Stricker, C. (2002) Exponential hedging and entropic penalties. Math. Finance 12, 99123.CrossRefGoogle Scholar
[8] Delbaen, F. and Schachermayer, W. (1994) A general version of the fundamental theorem of asset pricing. Mathematische Annalen 300, 463520.CrossRefGoogle Scholar
[9] Dickson, D.C.M. and Waters, H.R. (2003) Some optimal dividends problems. Astin Bulletin 34, 4974.CrossRefGoogle Scholar
[10] Duffie, D. (1996) Dynamic Asset Pricing Theory. 2nd Edition. Princeton University Press.Google Scholar
[11] Elliott, R.J. and Kopp, P.E. (2005) Mathematics of Financial Markets. 2nd Edition. Springer Finance, NY.Google Scholar
[12] Filipovic, D. and Zabczyk, J. (2002) Markovian term structure models in discrete time. Ann. Applied Prob. 12(2), 710729.CrossRefGoogle Scholar
[13] Föllmer, H. and Schied, A. (2004) Stochastic Finance: An Introduction in Discrete Time. 2nd Edition. De Gruyter Studies in Mathematics 27, Berlin.Google Scholar
[14] He, H. and Pearson, N.D. (1991) Consumption and portfolio policies with incomplete markets and short-sale constraints: the finite-dimensional case. Math. Finance 1(3), 110.CrossRefGoogle Scholar
[15] Henderson, V. (2002) Valuation of claims on nontraded assets using utility maximation. Math. Finance 12, 351373.CrossRefGoogle Scholar
[16] Henderson, V. (2005) Explicit solutions to an optimal portfolio choice problem with stochastic income. J. Economic Dynamics and Control 29, 12371266.CrossRefGoogle Scholar
[17] Henderson, V. and Hobson, D. (2007) Utility indifference pricing – an overview . To appear in: Volume on Indifference Pricing, Carmona, R. (Ed.), Princeton University Press.Google Scholar
[18] Hodges, S.D. and Neuberger, A. (1989) Optimal replication of contingent claims under transaction costs. Review of Futures Markets 8, 222239.Google Scholar
[19] Horst, U. and Muller, M. (2007) On the spanning property of risk bonds priced by equilibrium . To appear in Mathematics of Operations Research. CrossRefGoogle Scholar
[20] Ingersoll, J.E. (1987) Theory of Financial Decision Making. Rowman and Littlefield Publishers, Maryland.Google Scholar
[21] Karatzas, I. and Zitkovic, G. (2003) Optimal consumption from investment and random endowment in incomplete semimartingale markets, Ann. Prob. 31(4), 18211858.CrossRefGoogle Scholar
[22] Malamud, S. and Trubowitz, E. (2006) A unified approach to market incompleteness . Preprint, SSRN, http://papers.ssrn.com/sol3/papers.cfm?abstract_id = 990328. Google Scholar
[23] Malamud, S. and Trubowitz, E. (2006) Asset pricing for idiosyncratically incomplete markets . Preprint, SSRN, http://papers.ssrn.com/sol3/papers.cfm?abstract_id = 912788. Google Scholar
[24] Merton, R.C. (1971) Optimum consumption and portfolio rules in a continuous-time model. J. Economic Theory 3(4), 373413.Google Scholar
[25] Muermann, A. (2003) Actuarially consistent valuation of catastrophe derivatives . Wharton Financial Institution Center, working paper 0318.Google Scholar
[26] Musiela, M. and Zariphopoulou, T. (2004) An example of indifference prices under exponential preferences. Finance Stochast. 8, 229239.CrossRefGoogle Scholar
[27] Musiela, M. and Zariphopoulou, T. (2004) A valuation algorithm for indifference prices in incomplete markets. Finance Stochast. 8, 399414.CrossRefGoogle Scholar
[28] Pelsser, A. (2006) Pricing insurance contracts: an incomplete market approach . Notes ACFI seminar, 2 November 2006, University of Amsterdam.Google Scholar
[29] Rouge, R. and El Karoui, N. (2000) Pricing via utility maximization and entropy. Math. Finance 10, 259276.CrossRefGoogle Scholar
[30] Schachermayer, W. (1999) Utility Maximisation in Incomplete Markets. In: Stochastic Methods in Finance, Fritelli, M. and Runggaldier, W. (Eds.), Springer Lecture Notes in Mathematics 1856, 225288.Google Scholar
[31] Schmock, U. (1999) Estimating the value of the WinCAT coupons of the Winterthur Insurance Convertible Bond: a study of model risk. Astin Bulletin 29, 101163.CrossRefGoogle Scholar
[32] Tsanakas, A. and Christofides, N. (2006) Risk exchange with distorted probabilities. Astin Bulletin 36, 219244.CrossRefGoogle Scholar
[33] Wüthrich, M.V., Bühlmann, H. and Furrer, H. (2008) Market-Consistent Actuarial Valuation. EAA Lecture Notes, Springer.Google Scholar