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A class of globally solvable Markovian quadratic BSDE systems and applications

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  • Xing, Hao
  • Žitković, Gordan

Abstract

We establish global existence and uniqueness for a wide class of Markovian systems of backward stochastic differential equations (BSDE) with quadratic nonlinearities. This class is characterized by an abstract structural assumption on the generator, an a-priori local-boundedness property, and a locally-Hölder-continuous terminal condition. We present easily verifiable sufficient conditions for these assumptions and treat several applications, including stochastic equilibria in incomplete financial markets, stochastic differential games, and martingales on Riemannian manifolds

Suggested Citation

  • Xing, Hao & Žitković, Gordan, 2018. "A class of globally solvable Markovian quadratic BSDE systems and applications," LSE Research Online Documents on Economics 73440, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:73440
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    File URL: http://eprints.lse.ac.uk/73440/
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    References listed on IDEAS

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    1. Dmitry Kramkov & Sergio Pulido, 2014. "A system of quadratic BSDEs arising in a price impact model," Papers 1408.0916, arXiv.org, revised May 2016.
    2. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    3. Hu, Ying & Tang, Shanjian, 2016. "Multi-dimensional backward stochastic differential equations of diagonally quadratic generators," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1066-1086.
    4. El-Karoui, N. & Hamadène, S., 2003. "BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 145-169, September.
    5. Briand, Philippe & Elie, Romuald, 2013. "A simple constructive approach to quadratic BSDEs with or without delay," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 2921-2939.
    6. Frei, Christoph, 2014. "Splitting multidimensional BSDEs and finding local equilibria," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2654-2671.
    7. Jin Choi & Kasper Larsen, 2015. "Taylor approximation of incomplete Radner equilibrium models," Finance and Stochastics, Springer, vol. 19(3), pages 653-679, July.
    8. Subrahmanyam, Avanidhar, 1991. "Risk Aversion, Market Liquidity, and Price Efficiency," Review of Financial Studies, Society for Financial Studies, vol. 4(3), pages 416-441.
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    12. repec:spr:joptap:v:105:y:2000:i:3:d:10.1023_a:1004637022496 is not listed on IDEAS
    13. Dmitry Kramkov & Sergio Pulido, 2016. "A system of quadratic BSDEs arising in a price impact model," Post-Print hal-01147411, HAL.
    14. Tevzadze, Revaz, 2008. "Solvability of backward stochastic differential equations with quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 503-515, March.
    15. Çetin, Umut & Danilova, Albina, 2016. "Markovian Nash equilibrium in financial markets with asymmetric information and related forward-backward systems," LSE Research Online Documents on Economics 63259, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Kihun Nam, 2019. "Global Well-posedness of Non-Markovian Multidimensional Superquadratic BSDE," Papers 1912.03692, arXiv.org, revised Dec 2019.

    More about this item

    Keywords

    BSDE; backward stochastic differential equations; systems of BSDE; quadratic nonlinearities; stochastic equilibrium; martingales on manifolds; nonzero-sum stochastic games;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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