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Existence and uniqueness results for BSDEs with jumps: the whole nine yards

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  • Antonis Papapantoleon
  • Dylan Possamai
  • Alexandros Saplaouras

Abstract

This paper is devoted to obtaining a wellposedness result for multidimensional BSDEs with possibly unbounded random time horizon and driven by a general martingale in a filtration only assumed to satisfy the usual hypotheses, i.e. the filtration may be stochastically discontinuous. We show that for stochastic Lipschitz generators and unbounded, possibly infinite, time horizon, these equations admit a unique solution in appropriately weighted spaces. Our result allows in particular to obtain a wellposedness result for BSDEs driven by discrete--time approximations of general martingales.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1607.04214
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    Cited by:

    1. Chenguang Liu & Antonis Papapantoleon & Alexandros Saplaouras, 2024. "Convergence rates for Backward SDEs driven by L\'evy processes," Papers 2402.01337, arXiv.org.
    2. Sarah Bensalem & Nicolás Hernández-Santibáñez & Nabil Kazi-Tani, 2023. "A continuous-time model of self-protection," Finance and Stochastics, Springer, vol. 27(2), pages 503-537, April.
    3. Nam, Kihun, 2021. "Locally Lipschitz BSDE driven by a continuous martingale a path-derivative approach," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 376-411.
    4. Nicolás Hernández Santibáñez & Dylan Possamaï & Chao Zhou, 2020. "Bank Monitoring Incentives Under Moral Hazard and Adverse Selection," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 988-1035, March.
    5. Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2021. "Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models," Finance and Stochastics, Springer, vol. 25(4), pages 757-810, October.
    6. Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2020. "C\`adl\`ag semimartingale strategies for optimal trade execution in stochastic order book models," Papers 2006.05863, arXiv.org, revised Jul 2021.
    7. Camilo Hern'andez & Dylan Possamai, 2020. "Me, myself and I: a general theory of non-Markovian time-inconsistent stochastic control for sophisticated agents," Papers 2002.12572, arXiv.org, revised Jul 2021.
    8. Dylan Possamai & Nizar Touzi, 2020. "Is there a Golden Parachute in Sannikov's principal-agent problem?," Papers 2007.05529, arXiv.org, revised Oct 2022.
    9. Antonis Papapantoleon & Dylan Possamai & Alexandros Saplaouras, 2021. "Stability of backward stochastic differential equations: the general case," Papers 2107.11048, arXiv.org, revised Apr 2023.
    10. Sarah Bensalem & Nicolás Hernández Santibáñez & Nabil Kazi-Tani, 2022. "A Continuous-Time Model of Self-Protection," Working Papers hal-02974961, HAL.

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