Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0809.4781.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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.

Suggested Citation

  • Michail Anthropelos & Nikolaos E. Frangos & Stylianos Z. Xanthopoulos & Athanasios N. Yannacopoulos, 2008. "On contingent claims pricing in incomplete markets: A risk sharing approach," Papers 0809.4781, arXiv.org, revised Feb 2012.
    • Handle: RePEc:arx:papers:0809.4781
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0809.4781
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Marco Frittelli & Giacomo Scandolo, 2006. "Risk Measures And Capital Requirements For Processes," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 589-612, October.
    2. Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January.
    3. Julien Hugonnier & Dmitry Kramkov, 2004. "Optimal investment with random endowments in incomplete markets," Papers math/0405293, arXiv.org.
    4. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    5. M. Kaneko, 1984. "On interpersonal utility comparisons," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 1(3), pages 165-175, October.
    6. Basu, Kaushik, 1983. "Cardinal utility, utilitarianism, and a class of invariance axioms in welfare analysis," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 193-206, December.
    7. Freddy Delbaen & Peter Grandits & Thorsten Rheinländer & Dominick Samperi & Martin Schweizer & Christophe Stricker, 2002. "Exponential Hedging and Entropic Penalties," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 99-123, April.
    8. Michail Anthropelos & Gordan Zitkovic, 2008. "On Agents' Agreement and Partial-Equilibrium Pricing in Incomplete Markets," Papers 0803.2198, arXiv.org.
    9. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    10. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    11. 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.
    12. Marek Musiela & Thaleia Zariphopoulou, 2004. "An example of indifference prices under exponential preferences," Finance and Stochastics, Springer, vol. 8(2), pages 229-239, May.
    13. repec:dau:papers:123456789/361 is not listed on IDEAS
    14. Zinde-Walsh, Victoria, 1995. "ESTIMATION AND INFERENCE IN ECONOMETRICSRussell Davidson and James G. MacKinnon Oxford University Press, 1993," Econometric Theory, Cambridge University Press, vol. 11(3), pages 631-635, June.
    15. E. Jouini & W. Schachermayer & N. Touzi, 2008. "Optimal Risk Sharing For Law Invariant Monetary Utility Functions," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 269-292, April.
    16. Marco Frittelli, 2000. "The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 39-52, January.
    17. Magill, Michael & Shafer, Wayne, 1991. "Incomplete markets," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 30, pages 1523-1614, Elsevier.
    18. 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.
    19. Michael Mania & Martin Schweizer, 2005. "Dynamic exponential utility indifference valuation," Papers math/0508489, arXiv.org.
    20. Yuri M. Kabanov & Christophe Stricker, 2002. "On the optimal portfolio for the exponential utility maximization: remarks to the six‐author paper," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 125-134, April.
    21. Michael Magill & Martine Quinzii, 2002. "Theory of Incomplete Markets, Volume 1," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262632543, April.
    22. Richard Rouge & Nicole El Karoui, 2000. "Pricing Via Utility Maximization and Entropy," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 259-276, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Michail Anthropelos & Gordan Žitković, 2010. "Partial equilibria with convex capital requirements: existence, uniqueness and stability," Annals of Finance, Springer, vol. 6(1), pages 107-135, January.
    2. Michail Anthropelos & Gordan Zitkovic, 2009. "Partial Equilibria with Convex Capital Requirements: Existence, Uniqueness and Stability," Papers 0901.3318, arXiv.org.
    3. Mahan Tahvildari, 2021. "Forward indifference valuation and hedging of basis risk under partial information," Papers 2101.00251, arXiv.org.
    4. Knispel, Thomas & Laeven, Roger J.A. & Svindland, Gregor, 2016. "Robust optimal risk sharing and risk premia in expanding pools," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 182-195.
    5. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2015. "The pricing of contingent claims and optimal positions in asymptotically complete markets," Papers 1509.06210, arXiv.org, revised Sep 2016.
    6. Marina Santacroce & Paola Siri & Barbara Trivellato, 2023. "Forward Backward SDEs Systems for Utility Maximization in Jump Diffusion Models," Papers 2302.08253, arXiv.org.
    7. Kallsen Jan & Rheinländer Thorsten, 2011. "Asymptotic utility-based pricing and hedging for exponential utility," Statistics & Risk Modeling, De Gruyter, vol. 28(1), pages 17-36, March.
    8. Owari, Keita & 尾張, 圭太, 2008. "Robust Exponential Hedging and Indifference Valuation," Discussion Papers 2008-09, Graduate School of Economics, Hitotsubashi University.
    9. Roger J. A. Laeven & Mitja Stadje, 2014. "Robust Portfolio Choice and Indifference Valuation," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1109-1141, November.
    10. Guo, Ivan & Zhu, Song-Ping, 2017. "Equal risk pricing under convex trading constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 76(C), pages 136-151.
    11. Lixin Wu & Min Dai, 2009. "Pricing jump risk with utility indifference," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 177-186.
    12. Johannes Gerer & Gregor Dorfleitner, 2016. "A Note On Utility Indifference Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-17, September.
    13. Claudia Ceci & Anna Gerardi, 2011. "Utility indifference valuation for jump risky assets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 34(2), pages 85-120, November.
    14. Thorsten Rheinländer & Jenny Sexton, 2011. "Hedging Derivatives," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8062, August.
    15. Regis Houssou & Olivier Besson, 2010. "Indifference of Defaultable Bonds with Stochastic Intensity models," Papers 1003.4118, arXiv.org.
    16. Mark P. Owen & Gordan Žitković, 2009. "Optimal Investment With An Unbounded Random Endowment And Utility‐Based Pricing," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 129-159, January.
    17. Nicole EL KAROUI & Claudia RAVANELLI, 2008. "Cash Sub-additive Risk Measures and Interest Rate Ambiguity," Swiss Finance Institute Research Paper Series 08-09, Swiss Finance Institute.
    18. Barrieu, Pauline & El Karoui, Nicole, 2005. "Inf-convolution of risk measures and optimal risk transfer," LSE Research Online Documents on Economics 2829, London School of Economics and Political Science, LSE Library.
    19. Becherer, Dirk, 2003. "Rational hedging and valuation of integrated risks under constant absolute risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 1-28, August.
    20. d'Aspremont, Claude & Gevers, Louis, 2002. "Social welfare functionals and interpersonal comparability," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 10, pages 459-541, Elsevier.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:0809.4781. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.