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Forward Exponential Performances: Pricing and Optimal Risk Sharing

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  • Michail Anthropelos

Abstract

In a Markovian stochastic volatility model, we consider financial agents whose investment criteria are modelled by forward exponential performance processes. The problem of contingent claim indifference valuation is first addressed and a number of properties are proved and discussed. Special attention is given to the comparison between the forward exponential and the backward exponential utility indifference valuation. In addition, we construct the problem of optimal risk sharing in this forward setting and solve it when the agents' forward performance criteria are exponential.

Suggested Citation

  • Michail Anthropelos, 2011. "Forward Exponential Performances: Pricing and Optimal Risk Sharing," Papers 1109.3908, arXiv.org, revised Mar 2013.
  • Handle: RePEc:arx:papers:1109.3908
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    1. Tahir Choulli & Christophe Stricker & Jia Li, 2007. "Minimal Hellinger martingale measures of order q," Finance and Stochastics, Springer, vol. 11(3), pages 399-427, July.
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    3. M. Musiela & T. Zariphopoulou, 2009. "Portfolio choice under dynamic investment performance criteria," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 161-170.
    4. Michail Anthropelos & Gordan Zitkovic, 2008. "On Agents' Agreement and Partial-Equilibrium Pricing in Incomplete Markets," Papers 0803.2198, arXiv.org.
    5. He, Hua & Pearson, Neil D., 1991. "Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case," Journal of Economic Theory, Elsevier, vol. 54(2), pages 259-304, August.
    6. Gordan v{Z}itkovi'c, 2008. "A dual characterization of self-generation and exponential forward performances," Papers 0809.0739, arXiv.org, revised Dec 2009.
    7. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    8. repec:dau:papers:123456789/361 is not listed on IDEAS
    9. 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.
    10. Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.
    11. Damir Filipović & Gregor Svindland, 2008. "Optimal capital and risk allocations for law- and cash-invariant convex functions," Finance and Stochastics, Springer, vol. 12(3), pages 423-439, July.
    12. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    13. 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.
    14. 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.
    15. Susanne Klöppel & Martin Schweizer, 2007. "Dynamic Indifference Valuation Via Convex Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 599-627, October.
    16. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    17. Bühlmann, Hans & Jewell, William S., 1979. "Optimal Risk Exchanges," ASTIN Bulletin, Cambridge University Press, vol. 10(3), pages 243-262, December.
    18. Henderson, Vicky & Hobson, David, 2007. "Horizon-unbiased utility functions," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1621-1641, November.
    19. Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, April.
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    Cited by:

    1. Goncalo dos Reis & Vadim Platonov, 2020. "Forward utilities and Mean-field games under relative performance concerns," Papers 2005.09461, arXiv.org, revised Sep 2020.
    2. Qian Lin & Xianming Sun & Chao Zhou, 2019. "Horizon-unbiased Investment with Ambiguity," Papers 1904.09379, arXiv.org.
    3. Goncalo dos Reis & Vadim Platonov, 2020. "Forward utility and market adjustments in relative investment-consumption games of many players," Papers 2012.01235, arXiv.org, revised Mar 2022.
    4. Tahir Choulli & Junfeng Ma, 2013. "Explicit Description of HARA Forward Utilities and Their Optimal Portfolios," Papers 1307.0785, arXiv.org.

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