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On contingent claims pricing in incomplete markets: A risk sharing approach

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Author Info
Michail Anthropelos
Nikolaos E. Frangos
Stylianos Z. Xanthopoulos
Athanasios N. Yannacopoulos
Abstract

In an incomplete market setting, we consider two financial agents, who wish to price and trade a non-replicable contingent claim. Assuming that the agents are utility maximizers, we propose a transaction price which is a result of the minimization of a convex combination of their utility differences. We call this price the risk sharing price, we prove its existence for a large family of utility functions and we state some of its properties. As an example, we analyze extensively the case where both agents report exponential utility.

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File URL: http://arxiv.org/abs/0809.4781
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Paper provided by arXiv.org in its series Quantitative Finance Papers with number 0809.4781.

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Date of creation: Sep 2008
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Handle: RePEc:arx:papers:0809.4781

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  1. Julien Hugonnier & Dmitry Kramkov, 2004. "Optimal investment with random endowments in incomplete markets," Quantitative Finance Papers math/0405293, arXiv.org. [Downloadable!]
  2. Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January. [Downloadable!] (restricted)
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  3. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May. [Downloadable!] (restricted)
  4. Michael Mania & Martin Schweizer, 2005. "Dynamic exponential utility indifference valuation," Quantitative Finance Papers math/0508489, arXiv.org. [Downloadable!]
  5. Fishburn, Peter C., 1994. "Utility and subjective probability," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 39, pages 1397-1435 Elsevier. [Downloadable!] (restricted)
  6. Michael Magill & Martine Quinzii, 2002. "Theory of Incomplete Markets, Volume 1," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262632543, December.
  7. Marek Musiela & Thaleia Zariphopoulou, 2004. "An example of indifference prices under exponential preferences," Finance and Stochastics, Springer, vol. 8(2), pages 229-239, 05. [Downloadable!] (restricted)
  8. E. Jouini & W. Schachermayer & N. Touzi, 2008. "Optimal Risk Sharing For Law Invariant Monetary Utility Functions," Mathematical Finance, Blackwell Publishing, vol. 18(2), pages 269-292. [Downloadable!] (restricted)
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  9. Michail Anthropelos & Gordan Zitkovic, 2008. "On Agents' Agreement and Partial-Equilibrium Pricing in Incomplete Markets," Quantitative Finance Papers 0803.2198, arXiv.org. [Downloadable!]
  10. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April. [Downloadable!] (restricted)
  11. S. Z. Xanthopoulos & A. N. Yannacopoulos, 2008. "Scenarios For Price Determination In Incomplete Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(05), pages 415-445. [Downloadable!] (restricted)
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