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A Multivariate Extension of Equilibrium Pricing Transforms: The Multivariate Esscher and Wang Transforms for Pricing Financial and Insurance Risks

Published online by Cambridge University Press:  17 April 2015

Masaaki Kijima
Masaaki Kijima*
Affiliation:
Graduate School of Economics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan, Tel/Fax: +81-75-753-3511, E-Mail: [email protected]
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Abstract

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This paper proposes a multivariate extension of the equilibrium pricing transforms for pricing general financial and insurance risks. The multivariate Esscher and Wang transforms are derived from Bühlmann’s equilibrium pricing model (1980) under some assumptions on the aggregate risk. It is shown that the Esscher and Wang transforms coincide with each other when the underlying risks are normally distributed.

Keywords

Equilibrium pricingWang transformEsscher transformState price densityGaussian copula
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 36 , Issue 1 , May 2006 , pp. 269 - 283
Copyright
Copyright © ASTIN Bulletin 2006

References

Black, F. and Scholes, M. (1973) The pricing of options and corporate liabilities, Journal of Political Economy, 81, 637–654.CrossRefGoogle Scholar
Bühlmann, H. (1980) An economic premium principle, Astin Bulletin, 11, 52–60.CrossRefGoogle Scholar
Gerber, H.U. and Shiu, E.S.W. (1994) Option pricing by Esscher transforms, Transactions of the Society of Actuaries, 46, 99–140.Google Scholar
Harrison, M.J. and Kreps, D. (1979) Martingales and arbitrage in multiperiod securities market, Journal of Economic Theory, 20, 381–408.CrossRefGoogle Scholar
Iwaki, H., Kijima, M. and Morimoto, Y. (2001) An economic premium principle in a multi-period economy, Insurance: Mathematics and Economics, 28, 325–339.Google Scholar
Jensen, L.J. (1995) Saddlepoint Approximation, Oxford Science Publications, Oxford.Google Scholar
Kijima, M. (2002) Stochastic Processes with Applications to Finance, Chapman & Hall, London.CrossRefGoogle Scholar
Kijima, M. and Muromachi, Y. (2001) Pricing of equity swaps in a stochastic interest rate economy. Journal of Derivatives, 8, 19–35.CrossRefGoogle Scholar
Kijima, M. and Muromachi, Y. (2006) On the Wang transform with fat-tail distributions. In Preparation.Google Scholar
Kijima, M. and Ohnishi, M. (1996) Portfolio selection problems via the bivariate characterization of stochastic dominance relations, Mathematical Finance, 6, 237–277.CrossRefGoogle Scholar
Marshall, A.W. and Olkin, I. (1988) Families of multivariate distributions. Journal of the American Statistical Association, 83, 834–841.CrossRefGoogle Scholar
Nelsen, R.B. (1999) An Introduction to Copulas, Springer, New York.CrossRefGoogle Scholar
Pliska, S.R. (1997) Introduction to Mathematical Finance: Discrete Time Models, Blackwell, Cambridge.Google Scholar
Tong, Y.L. (1990) The Multivariate Normal Distribution, Springer, New York.CrossRefGoogle Scholar
Wang, S.S. (2000) A class of distortion operators for pricing financial and insurance risks, Journal of Risk and Insurance, 67, 15–36.CrossRefGoogle Scholar
Wang, S.S. (2002) A universal framework for pricing financial and insurance risks, Astin Bulletin, 32, 213–234.CrossRefGoogle Scholar
Wang, S.S. (2003) Equilibrium pricing transforms: New results using Bühlmann’s 1980 economic model, Astin Bulletin, 33, 57–73.CrossRefGoogle Scholar
Wang, S.S. (2005) Normalized exponential tilting: Pricing and measuring multivariate risks, Working Paper, Georgia State University.Google Scholar