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Multi-agent investment in incomplete markets

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  • Jianming Xia

Abstract

The problem of the expected utility maximization in incomplete markets for a single agent is well understood in a fairly general setting. This paper studies the problem for the multi-agent case. For this case a cooperative investment game is posed as follows: firstly collect all agents’ capital together at the initial time, then invest the total capital in a trading strategy, and finally divide the terminal wealth of the trading strategy and each of them gets a part. We give a characterization of Pareto optimal cooperative strategies and a characterization of situations where cooperation strictly Pareto dominates non cooperation, and prove that the core of the cooperative investment game is non-empty under mild conditions using Scarf theorem. Copyright Springer-Verlag Berlin/Heidelberg 2004

Suggested Citation

  • Jianming Xia, 2004. "Multi-agent investment in incomplete markets," Finance and Stochastics, Springer, vol. 8(2), pages 241-259, May.
    • Handle: RePEc:spr:finsto:v:8:y:2004:i:2:p:241-259
    DOI: 10.1007/s00780-003-0115-2
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    Citations

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    Cited by:

    1. Pazdera, Jaroslav, 2018. "Essays on risk exchanges within a collective," Other publications TiSEM 52e0c35f-9009-454d-81af-5, Tilburg University, School of Economics and Management.
    2. Bogdan Grechuk & Michael Zabarankin, 2017. "Synergy effect of cooperative investment," Annals of Operations Research, Springer, vol. 249(1), pages 409-431, February.
    3. Nicole Branger & An Chen & Antje Mahayni & Thai Nguyen, 2023. "Optimal collective investment: an analysis of individual welfare," Mathematics and Financial Economics, Springer, volume 17, number 5, December.
    4. Pazdera, Jaroslav & Schumacher, Johannes M. & Werker, Bas J.M., 2016. "Cooperative investment in incomplete markets under financial fairness," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 394-406.
    5. An Chen & Thai Nguyen & Manuel Rach, 2021. "A collective investment problem in a stochastic volatility environment: The impact of sharing rules," Annals of Operations Research, Springer, vol. 302(1), pages 85-109, July.
    6. 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.
    7. Bogdan Grechuk & Andrzej Palczewski & Jan Palczewski, 2018. "On the solution uniqueness in portfolio optimization and risk analysis," Papers 1810.11299, arXiv.org, revised Oct 2020.
    8. Chen, An & Nguyen, Thai & Rach, Manuel, 2021. "Optimal collective investment: The impact of sharing rules, management fees and guarantees," Journal of Banking & Finance, Elsevier, vol. 123(C).
    9. Zhou, Qing & Wu, Weixing & Wang, Zengwu, 2008. "Cooperative hedging with a higher interest rate for borrowing," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 609-616, April.
    10. Keisuke Kizaki & Taiga Saito & Akihiko Takahashi, 2023. "A multi-agent incomplete equilibrium model and its applications to reinsurance pricing and life-cycle investment (Forthcoming in "Insurance: Mathematics and Economics")," CARF F-Series CARF-F-576, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    11. Claudia Kluppelberg & Miriam Isabel Seifert, 2016. "Conditional loss probabilities for systems of economic agents sharing light-tailed claims with analysis of portfolio diversification benefits," Papers 1612.07132, arXiv.org.
    12. Grechuk, Bogdan, 2023. "Extended gradient of convex function and capital allocation," European Journal of Operational Research, Elsevier, vol. 305(1), pages 429-437.
    13. Pazdera, Jaroslav & Schumacher, Johannes M. & Werker, Bas J.M., 2017. "The composite iteration algorithm for finding efficient and financially fair risk-sharing rules," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 122-133.
    14. Claudia Klüppelberg & Miriam Isabel Seifert, 2019. "Financial risk measures for a network of individual agents holding portfolios of light-tailed objects," Finance and Stochastics, Springer, vol. 23(4), pages 795-826, October.

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