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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: kijima_daiwa@econ.kyoto-u.ac.jp
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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

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