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Solvability of backward stochastic differential equations with quadratic growth

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  • Tevzadze, Revaz

Abstract

We prove the existence of the unique solution of a general backward stochastic differential equation with quadratic growth driven by martingales. A kind of comparison theorem is also proved.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:spapps:v:118:y:2008:i:3:p:503-515
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    References listed on IDEAS

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    1. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    2. Michael Mania & Martin Schweizer, 2005. "Dynamic exponential utility indifference valuation," Papers math/0508489, arXiv.org.
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    Cited by:

    1. repec:eee:spapps:v:128:y:2018:i:6:p:2083-2130 is not listed on IDEAS
    2. Jia, Guangyan & Zhang, Na, 2015. "Quadratic g-convexity, C-convexity and their relationships," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2272-2294.
    3. Michael Mania & Marina Santacroce, 2010. "Exponential utility maximization under partial information," Finance and Stochastics, Springer, vol. 14(3), pages 419-448, September.
    4. Ying Hu & Gechun Liang & Shanjian Tang, 2018. "Systems of infinite horizon and ergodic BSDE arising in regime switching forward performance processes," Papers 1807.01816, arXiv.org, revised Jul 2018.
    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. Jana Bielagk & Arnaud Lionnet & Goncalo Dos Reis, 2015. "Equilibrium pricing under relative performance concerns," Papers 1511.04218, arXiv.org, revised Feb 2017.
    7. Lionnet, Arnaud, 2014. "Some results on general quadratic reflected BSDEs driven by a continuous martingale," Stochastic Processes and their Applications, Elsevier, vol. 124(3), pages 1275-1302.
    8. Covello, D. & Santacroce, M., 2010. "Power utility maximization under partial information: Some convergence results," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 2016-2036, September.
    9. 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.
    10. Frei, Christoph, 2014. "Splitting multidimensional BSDEs and finding local equilibria," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2654-2671.
    11. Vicky Henderson & Gechun Liang, 2014. "Pseudo linear pricing rule for utility indifference valuation," Finance and Stochastics, Springer, vol. 18(3), pages 593-615, July.
    12. Michael Mania & Marina Santacroce, 2008. "Exponential Utility Maximization under Partial Information," ICER Working Papers - Applied Mathematics Series 24-2008, ICER - International Centre for Economic Research.
    13. Dirk Becherer & Martin Buttner & Klebert Kentia, 2016. "On the monotone stability approach to BSDEs with jumps: Extensions, concrete criteria and examples," Papers 1607.06644, arXiv.org, revised May 2018.
    14. Revaz Tevzadze & Teimuraz Toronjadze & Tamaz Uzunashvili, 2013. "Robust utility maximization for a diffusion market model with misspecified coefficients," Finance and Stochastics, Springer, vol. 17(3), pages 535-563, July.
    15. R. Tevzadze & T. Toronjadze, 2009. "Robust utility maximization for diffusion market model with misspecified coefficients," Papers 0911.3043, arXiv.org.
    16. Jana Bielagk & Arnaud Lionnet & Gonçalo Dos Reis, 2015. "Equilibrium pricing under relative performance concerns," Working Papers hal-01245812, HAL.
    17. Antonis Papapantoleon & Dylan Possamai & Alexandros Saplaouras, 2016. "Existence and uniqueness results for BSDEs with jumps: the whole nine yards," Papers 1607.04214, arXiv.org, revised Nov 2018.
    18. 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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