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Buhlmann’s Economic Premium Principle in The Presence of Transaction Costs

Author

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  • Masaaki Kijima

    (Graduate School of Social Sciences, Tokyo Metropolitan University)

  • Akihisa Tamura

    (Department of Mathematics, Keio University)

Abstract

This paper examines the B¨uhlmann’s equilibrium pricing model (1980) in the presence of transaction cost and derives the (multivariate) Esscher transform within the framework under some assumptions. The result reveals that the Esscher transform is an appropriate probability transform for the pricing of insurance risks even in the market with transaction costs.

Suggested Citation

  • Masaaki Kijima & Akihisa Tamura, 2014. "Buhlmann’s Economic Premium Principle in The Presence of Transaction Costs," KIER Working Papers 893, Kyoto University, Institute of Economic Research.
    • Handle: RePEc:kyo:wpaper:893
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    References listed on IDEAS

    as
    1. Kijima, Masaaki & Muromachi, Yukio, 2008. "An extension of the Wang transform derived from Bühlmann's economic premium principle for insurance risk," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 887-896, June.
    2. Malamud, Semyon & Trubowitz, Eugene & Wüthrich, Mario V., 2008. "Market Consistent Pricing of Insurance Products," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 483-526, November.
    3. Wang, Shaun S., 2003. "Equilibrium Pricing Transforms: New Results Using Buhlmann’s 1980 Economic Model," ASTIN Bulletin, Cambridge University Press, vol. 33(1), pages 57-73, May.
    4. Kijima, Masaaki, 2006. "A Multivariate Extension of Equilibrium Pricing Transforms: The Multivariate Esscher and Wang Transforms for Pricing Financial and Insurance Risks," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 269-283, May.
    5. Hojgaard, Bjarne & Taksar, Michael, 1998. "Optimal proportional reinsurance policies for diffusion models with transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 41-51, May.
    6. Wang, Shaun S., 2002. "A Universal Framework for Pricing Financial and Insurance Risks," ASTIN Bulletin, Cambridge University Press, vol. 32(2), pages 213-234, November.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    8. Knut K. Aase, 2002. "Equilibrium Pricing in the Presence of Cumulative Dividends Following a Diffusion," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 173-198, July.
    9. He, Lin & Liang, Zongxia, 2009. "Optimal financing and dividend control of the insurance company with fixed and proportional transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 88-94, February.
    10. Aase, Knut K., 1993. "Equilibrium in a Reinsurance Syndicate; Existence, Uniqueness and Characterization," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 185-211, November.
    11. Chiaki Hara, 2013. "Asset Prices, Trading Volumes, and Investor Welfare in Markets with Transaction Costs　," KIER Working Papers 862, Kyoto University, Institute of Economic Research.
    12. Tsanakas, Andreas & Christofides, Nicos, 2006. "Risk Exchange with Distorted Probabilities," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 219-243, May.
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    More about this item

    Keywords

    Equilibrium pricing; Equilibrium allocation; Incomplete market; Esscher transform; Transaction cost;
    All these keywords.

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