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An incomplete equilibrium with a stochastic annuity

Author

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  • Kim Weston

    (Rutgers University)

  • Gordan Žitković

    (The University of Texas at Austin)

Abstract

We prove the global existence of an incomplete, continuous-time finite-agent Radner equilibrium in which exponential agents optimise their expected utility over both running consumption and terminal wealth. The market consists of a traded annuity, and along with unspanned income, the market is incomplete. Set in a Brownian framework, the income is driven by a multidimensional diffusion and in particular includes mean-reverting dynamics. The equilibrium is characterised by a system of fully coupled quadratic backward stochastic differential equations, a solution to which is proved to exist under Markovian assumptions. We also show that the equilibrium allocations lead to Pareto-optimal allocations only in exceptional situations.

Suggested Citation

  • Kim Weston & Gordan Žitković, 2020. "An incomplete equilibrium with a stochastic annuity," Finance and Stochastics, Springer, vol. 24(2), pages 359-382, April.
    • Handle: RePEc:spr:finsto:v:24:y:2020:i:2:d:10.1007_s00780-020-00415-6
    DOI: 10.1007/s00780-020-00415-6
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Masaaki Fujii & Akihiko Takahashi, 2022. "Equilibrium Price Formation with a Major Player and its Mean Field Limit (Forthcoming in ESAIM: Control, Optimization and Calculus of Variations)(Revised version of CARF-F-509)," CARF F-Series CARF-F-533, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. 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.
    5. Kim Weston, 2022. "Existence of an equilibrium with limited participation," Papers 2206.12399, arXiv.org.
    6. Masaaki Fujii & Akihiko Takahashi, 2021. "Strong Convergence to the Mean-Field Limit of A Finite Agent Equilibrium," CIRJE F-Series CIRJE-F-1180, CIRJE, Faculty of Economics, University of Tokyo.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.

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    More about this item

    Keywords

    Incomplete markets; Radner equilibrium; Annuity; BSDE; Systems of BSDEs; Unspanned income;
    All these keywords.

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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