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An example of a stochastic equilibrium with incomplete markets

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  • Gordan Žitković

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  • Gordan Žitković, 2012. "An example of a stochastic equilibrium with incomplete markets," Finance and Stochastics, Springer, vol. 16(2), pages 177-206, April.
    • Handle: RePEc:spr:finsto:v:16:y:2012:i:2:p:177-206
    DOI: 10.1007/s00780-011-0161-0
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    References listed on IDEAS

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    1. Darrell Duffie & Chi-Fu Huang, 2005. "Implementing Arrow-Debreu Equilibria By Continuous Trading Of Few Long-Lived Securities," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 4, pages 97-127, World Scientific Publishing Co. Pte. Ltd..
    2. Basak, Suleyman & Cuoco, Domenico, 1998. "An Equilibrium Model with Restricted Stock Market Participation," The Review of Financial Studies, Society for Financial Studies, vol. 11(2), pages 309-341.
    3. Duffie, Darrell & Zame, William, 1989. "The Consumption-Based Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 57(6), pages 1279-1297, November.
    4. Larsen, Kasper & Zitkovic, Gordan, 2007. "Stability of utility-maximization in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1642-1662, November.
    5. Herbert E. Scarf, 1967. "The Approximation of Fixed Points of a Continuous Mapping," Cowles Foundation Discussion Papers 216R, Cowles Foundation for Research in Economics, Yale University.
    6. Kasper Larsen & Gordan Zitkovic, 2007. "Stability of utility-maximization in incomplete markets," Papers 0706.0474, arXiv.org.
    7. Michael Magill & Martine Quinzii, 2002. "Theory of Incomplete Markets, Volume 1," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262632543, April.
    8. Ioannis Karatzas & John P. Lehoczky & Steven E. Shreve, 1991. "Equilibrium Models With Singular Asset Prices," Mathematical Finance, Wiley Blackwell, vol. 1(3), pages 11-29, July.
    9. Elyès Jouini & Clotilde Napp, 2004. "Convergence of utility functions and convergence of optimal strategies," Finance and Stochastics, Springer, vol. 8(1), pages 133-144, January.
    10. 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.
    11. 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.
    12. Ioannis Karatzas & John P. Lehoczky & Steven E. Shreve, 1990. "Existence and Uniqueness of Multi-Agent Equilibrium in a Stochastic, Dynamic Consumption/Investment Model," Mathematics of Operations Research, INFORMS, vol. 15(1), pages 80-128, February.
    13. Robert M. Anderson & Roberto C. Raimondo, 2008. "Equilibrium in Continuous-Time Financial Markets: Endogenously Dynamically Complete Markets," Econometrica, Econometric Society, vol. 76(4), pages 841-907, July.
    14. Duffie, Darrell, 1986. "Stochastic Equilibria: Existence, Spanning Number, and the 'No Expected Financial Gain from Trade' Hypothesis," Econometrica, Econometric Society, vol. 54(5), pages 1161-1183, September.
    15. Rose-Anne Dana & Monique Pontier, 1992. "On the Existence of an Arrow-Radner Equilibrium in the Case of Complete Markets. A Remark," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 148-163, February.
    16. Gordan Žitković, 2006. "Financial equilibria in the semimartingale setting: Complete markets and markets with withdrawal constraints," Finance and Stochastics, Springer, vol. 10(1), pages 99-119, January.
    17. Kasper Larsen, 2009. "Continuity Of Utility‐Maximization With Respect To Preferences," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 237-250, April.
    18. Herbert E. Scarf, 1967. "On the Computation of Equilibrium Prices," Cowles Foundation Discussion Papers 232, Cowles Foundation for Research in Economics, Yale University.
    19. repec:dau:papers:123456789/355 is not listed on IDEAS
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    Citations

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    Cited by:

    1. Xiao Chen & Jin Hyuk Choi & Kasper Larsen & Duane J. Seppi, 2019. "Resolving asset pricing puzzles using price-impact," Papers 1910.02466, arXiv.org, revised Jun 2020.
    2. Masaaki Fujii & Akihiko Takahashi, 2021. "Equilibrium Price Formation with a Major Player and its Mean Field Limit," CARF F-Series CARF-F-509, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Martin Herdegen & Johannes Muhle-Karbe, 2018. "Stability of Radner equilibria with respect to small frictions," Finance and Stochastics, Springer, vol. 22(2), pages 443-502, April.
    4. Masaaki Fujii & Akihiko Takahashi, 2020. "A Finite Agent Equilibrium in an Incomplete Market and its Strong Convergence to the Mean-Field Limit," CARF F-Series CARF-F-495, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    5. Masaaki Fujii & Akihiko Takahashi, 2020. "A Finite Agent Equilibrium in an Incomplete Market and its Strong Convergence to the Mean-Field Limit," CIRJE F-Series CIRJE-F-1156, CIRJE, Faculty of Economics, University of Tokyo.
    6. Bayraktar, Erhan & Kravitz, Ross, 2013. "Stability of exponential utility maximization with respect to market perturbations," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1671-1690.
    7. Luis Escauriaza & Daniel C. Schwarz & Hao Xing, 2020. "Radner equilibrium and systems of quadratic BSDEs with discontinuous generators," Papers 2008.03500, arXiv.org, revised May 2021.
    8. Kizaki, Keisuke & Saito, Taiga & Takahashi, Akihiko, 2024. "A multi-agent incomplete equilibrium model and its applications to reinsurance pricing and life-cycle investment," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 132-155.
    9. Masaaki Fujii & Masashi Sekine, 2024. "Mean Field Equilibrium Asset Pricing Model with Habit Formation," CIRJE F-Series CIRJE-F-1229, CIRJE, Faculty of Economics, University of Tokyo.
    10. Masaaki Fujii & Masashi Sekine, 2024. "Mean field equilibrium asset pricing model with habit formation," Papers 2406.02155, arXiv.org, revised Nov 2024.
    11. Robert Jarrow, 2018. "Asset market equilibrium with liquidity risk," Annals of Finance, Springer, vol. 14(2), pages 253-288, May.
    12. Masaaki Fujii & Akihiko Takahashi, 2021. "``Equilibrium Price Formation with a Major Player and its Mean Field Limit''," CIRJE F-Series CIRJE-F-1162, CIRJE, Faculty of Economics, University of Tokyo.
    13. Kim Weston & Gordan Žitković, 2020. "An incomplete equilibrium with a stochastic annuity," Finance and Stochastics, Springer, vol. 24(2), pages 359-382, April.
    14. Jin Choi & Kasper Larsen, 2015. "Taylor approximation of incomplete Radner equilibrium models," Finance and Stochastics, Springer, vol. 19(3), pages 653-679, July.
    15. Bruno Bouchard & Masaaki Fukasawa & Martin Herdegen & Johannes Muhle-Karbe, 2018. "Equilibrium Returns with Transaction Costs," Post-Print hal-01569408, HAL.
    16. Lukas Gonon & Johannes Muhle-Karbe & Xiaofei Shi, 2019. "Asset Pricing with General Transaction Costs: Theory and Numerics," Papers 1905.05027, arXiv.org, revised Apr 2020.
    17. Bruno Bouchard & Masaaki Fukasawa & Martin Herdegen & Johannes Muhle-Karbe, 2017. "Equilibrium Returns with Transaction Costs," Papers 1707.08464, arXiv.org, revised Apr 2018.
    18. Masaaki Fujii & Akihiko Takahashi, 2021. "Equilibrium Price Formation with a Major Player and its Mean Field Limit," Papers 2102.10756, arXiv.org, revised Feb 2022.
    19. Xiao Chen & Jin Hyuk Choi & Kasper Larsen & Duane J. Seppi, 2023. "Price impact in Nash equilibria," Finance and Stochastics, Springer, vol. 27(2), pages 305-340, April.
    20. Bruno Bouchard & Masaaki Fukasawa & Martin Herdegen & Johannes Muhle-Karbe, 2018. "Equilibrium returns with transaction costs," Finance and Stochastics, Springer, vol. 22(3), pages 569-601, July.
    21. Masaaki Fujii & Masashi Sekine, 2024. "Mean field equilibrium asset pricing model with habit formation (Forthcoming in Asia-Pacific Financial Markets)," CARF F-Series CARF-F-587, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Nov 2024.
    22. Masaaki Fujii & Akihiko Takahashi, 2020. "Strong Convergence to the Mean-Field Limit of A Finite Agent Equilibrium," Papers 2010.09186, arXiv.org, revised Dec 2021.
    23. Constantinos Kardaras & Hao Xing & Gordan v{Z}itkovi'c, 2015. "Incomplete stochastic equilibria for dynamic monetary utility," Papers 1505.07224, arXiv.org, revised Feb 2017.

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    More about this item

    Keywords

    Equilibrium; Exponential utility; Incomplete markets; Mathematical finance; 91G80; 35K59; C62; G11;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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