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A valuation algorithm for indifference prices in incomplete markets

Author

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  • Marek Musiela
  • Thaleia Zariphopoulou

Abstract

A probabilistic iterative algorithm is constructed for indifference prices of claims in a multiperiod incomplete model. At each time step, a nonlinear pricing functional is applied that isolates and prices separately the two types of risk. It is represented solely in terms of risk aversion and the pricing measure, a martingale measure that preserves the conditional distribution of unhedged risks, given the hedgeable ones, from their historical counterparts. Copyright Springer-Verlag Berlin/Heidelberg 2004

Suggested Citation

  • Marek Musiela & Thaleia Zariphopoulou, 2004. "A valuation algorithm for indifference prices in incomplete markets," Finance and Stochastics, Springer, vol. 8(3), pages 399-414, August.
    • Handle: RePEc:spr:finsto:v:8:y:2004:i:3:p:399-414
    DOI: 10.1007/s00780-003-0117-0
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    Citations

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    Cited by:

    1. Gang-Zhi Fan & Ming Pu & Seow Ong, 2012. "Optimal Portfolio Choices, House Risk Hedging and the Pricing of Forward House Transactions," The Journal of Real Estate Finance and Economics, Springer, vol. 45(1), pages 3-29, June.
    2. Lixin Wu & Min Dai, 2009. "Pricing jump risk with utility indifference," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 177-186.
    3. Traian A. Pirvu & Huayue Zhang, 2012. "A Multi Period Equilibrium Pricing Model," Papers 1205.6193, arXiv.org.
    4. Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January.
    5. Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.
    6. Rubtsov, Alexey, 2016. "Model misspecification and pricing of illiquid claims," Finance Research Letters, Elsevier, vol. 18(C), pages 242-249.
    7. Gang-Zhi Fan & Zsuzsa Huszár & Weina Zhang, 2013. "The Relationships between Real Estate Price and Expected Financial Asset Risk and Return: Theory and Empirical Evidence," The Journal of Real Estate Finance and Economics, Springer, vol. 46(4), pages 568-595, May.
    8. Ludkovski, Michael & Young, Virginia R., 2008. "Indifference pricing of pure endowments and life annuities under stochastic hazard and interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 14-30, February.
    9. Alet Roux & Zhikang Xu, 2019. "Optimal investment and contingent claim valuation with exponential disutility under proportional transaction costs," Papers 1909.06260, arXiv.org, revised May 2021.
    10. M. R. Grasselli, 2005. "Nonlinearity, correlation and the valuation of employee stock options," Papers math/0511234, arXiv.org.
    11. Dilip Madan, 2011. "Joint risk-neutral laws and hedging," IISE Transactions, Taylor & Francis Journals, vol. 43(12), pages 840-850.
    12. Liu, Haibo & Tang, Qihe & Yuan, Zhongyi, 2021. "Indifference pricing of insurance-linked securities in a multi-period model," European Journal of Operational Research, Elsevier, vol. 289(2), pages 793-805.
    13. Antoon Pelsser & Mitja Stadje, 2014. "Time-Consistent And Market-Consistent Evaluations," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 25-65, January.
    14. Dhaene, Jan & Stassen, Ben & Barigou, Karim & Linders, Daniël & Chen, Ze, 2017. "Fair valuation of insurance liabilities: Merging actuarial judgement and market-consistency," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 14-27.
    15. Braouezec, Yann & Joliet, Robert, 2019. "Valuing an investment project using no-arbitrage and the alpha-maxmin criteria: From Knightian uncertainty to risk," Economics Letters, Elsevier, vol. 178(C), pages 111-115.
    16. Ulrich Horst & Matthias Müller, 2007. "On the Spanning Property of Risk Bonds Priced by Equilibrium," Mathematics of Operations Research, INFORMS, vol. 32(4), pages 784-807, November.
    17. Fan, Gang-Zhi & Pu, Ming & Deng, Xiaoying & Ong, Seow Eng, 2018. "Optimal portfolio choices and the determination of housing rents under housing market uncertainty," Journal of Housing Economics, Elsevier, vol. 41(C), pages 200-217.
    18. Marek Musiela, 2022. "My journey through finance and stochastics," Finance and Stochastics, Springer, vol. 26(1), pages 33-58, January.
    19. Ming Pu & Gang-Zhi Fan & Seow Ong, 2012. "Heterogeneous Agents and the Indifference Pricing of Property Index Linked Swaps," The Journal of Real Estate Finance and Economics, Springer, vol. 44(4), pages 543-569, May.
    20. Yunhong Li & Zuo Quan Xu & Xun Yu Zhou, 2023. "Robust utility maximization with intractable claims," Papers 2304.06938, arXiv.org, revised Jul 2023.
    21. Rubtsov, Alexey & Xu, Wei & Šević, Aleksandar & Šević, Željko, 2021. "Price of climate risk hedging under uncertainty," Technological Forecasting and Social Change, Elsevier, vol. 165(C).
    22. Yunhong Li & Zuo Quan Xu & Xun Yu Zhou, 2023. "Robust utility maximisation with intractable claims," Finance and Stochastics, Springer, vol. 27(4), pages 985-1015, October.
    23. Chen, An & Pelsser, Antoon & Vellekoop, Michel, 2011. "Modeling non-monotone risk aversion using SAHARA utility functions," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2075-2092, September.

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