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A general non-existence result for linear BSDEs driven by Gaussian processes

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  • Bender, Christian
  • Viitasaari, Lauri

Abstract

In this paper, we study linear backward stochastic differential equations driven by a class of centered Gaussian non-martingales, including fractional Brownian motion with Hurst parameter H∈(0,1)∖{12}. We show that, for every choice of deterministic coefficient functions, there is a square integrable terminal condition such that the equation has no solution.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:4:p:1204-1233
    DOI: 10.1016/j.spa.2016.07.012
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    References listed on IDEAS

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    1. Bender, Christian, 2014. "Backward SDEs driven by Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2892-2916.
    2. León, Jorge A. & Nualart, David, 2005. "An extension of the divergence operator for Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 481-492, March.
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