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Infinite horizon forward-backward stochastic differential equations

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  • Peng, Shige
  • Shi, Yufeng

Abstract

A class of systems of infinite horizon forward-backward stochastic differential equations is investigated. Under some monotonicity assumptions, the existence and uniqueness results are established by means of a homotopy method. The global exponential asymptotical stability is also obtained. A comparison theorem is given.

Suggested Citation

  • Peng, Shige & Shi, Yufeng, 2000. "Infinite horizon forward-backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 85(1), pages 75-92, January.
    • Handle: RePEc:eee:spapps:v:85:y:2000:i:1:p:75-92
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    References listed on IDEAS

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    1. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    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. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
    4. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
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    Cited by:

    1. Guo, Dongmei & Ji, Shaolin & Zhao, Huaizhong, 2006. "On the solvability of infinite horizon forward-backward stochastic differential equations with absorption coefficients," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 1954-1960, December.
    2. Yannacopoulos, Athanasios N., 2008. "Rational expectations models: An approach using forward-backward stochastic differential equations," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 251-276, February.
    3. Gregory Gagnon, 2019. "Vanishing central bank intervention in stochastic impulse control," Annals of Finance, Springer, vol. 15(1), pages 125-153, March.
    4. Yin, Juliang, 2008. "On solutions of a class of infinite horizon FBSDEs," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2412-2419, October.
    5. Guangchen Wang & Hua Xiao, 2015. "Arrow Sufficient Conditions for Optimality of Fully Coupled Forward–Backward Stochastic Differential Equations with Applications to Finance," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 639-656, May.
    6. Delbaen, Freddy & Qiu, Jinniao & Tang, Shanjian, 2015. "Forward–backward stochastic differential systems associated to Navier–Stokes equations in the whole space," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2516-2561.
    7. Gregory Gagnon, 2012. "Exchange rate bifurcation in a stochastic evolutionary finance model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 35(1), pages 29-58, May.
    8. Liu, Jingmei & Liang, Xiao & Xu, Juanjuan, 2021. "Solution to the forward and backward stochastic difference equations with asymmetric information and application," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    9. Xanthi-Isidora Kartala & Nikolaos Englezos & Athanasios N. Yannacopoulos, 2020. "Future Expectations Modeling, Random Coefficient Forward–Backward Stochastic Differential Equations, and Stochastic Viscosity Solutions," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 403-433, May.

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