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Backward SDEs driven by Gaussian processes

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  • Bender, Christian

Abstract

In this paper we discuss existence and uniqueness results for BSDEs driven by centered Gaussian processes. Compared to the existing literature on Gaussian BSDEs, which mainly treats fractional Brownian motion with Hurst parameter H>1/2, our main contributions are: (i) Our results cover a wide class of Gaussian processes as driving processes including fractional Brownian motion with arbitrary Hurst parameter H∈(0,1); (ii) the assumptions on the generator f are mild and include e.g. the case when f has (super-)quadratic growth in z; (iii) the proofs are based on transferring the problem to an auxiliary BSDE driven by a Brownian motion.

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  • Bender, Christian, 2014. "Backward SDEs driven by Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2892-2916.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:9:p:2892-2916
    DOI: 10.1016/j.spa.2014.03.013
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    1. Robert J. Elliott & John Van Der Hoek, 2003. "A General Fractional White Noise Theory And Applications To Finance," Mathematical Finance, Wiley Blackwell, vol. 13(2), pages 301-330, April.
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    4. Jost, Céline, 2006. "Transformation formulas for fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1341-1357, October.
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    6. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
    7. Biagini, Francesca & Hu, Yaozhong & Øksendal, Bernt & Sulem, Agnès, 0. "A stochastic maximum principle for processes driven by fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 100(1-2), pages 233-253, July.
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    Cited by:

    1. Yu, Xianye & Zhang, Mingbo, 2020. "Backward stochastic differential equations driven by fractional noise with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 159(C).
    2. Wen, Jiaqiang & Shi, Yufeng, 2017. "Anticipative backward stochastic differential equations driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 118-127.
    3. Bender, Christian & Viitasaari, Lauri, 2017. "A general non-existence result for linear BSDEs driven by Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 127(4), pages 1204-1233.
    4. Sin, Myong-Guk & Ri, Kyong-Il & Kim, Kyong-Hui, 2022. "Existence and uniqueness of solution for coupled fractional mean-field forward–backward stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 190(C).
    5. Bender, Christian & Knobloch, Robert & Oberacker, Philip, 2015. "A generalised Itō formula for Lévy-driven Volterra processes," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 2989-3022.
    6. Douissi, Soukaina & Wen, Jiaqiang & Shi, Yufeng, 2019. "Mean-field anticipated BSDEs driven by fractional Brownian motion and related stochastic control problem," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 282-298.

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