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Generalized BSDEs with random time horizon in a progressively enlarged filtration

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  • Anna Aksamit
  • Libo Li
  • Marek Rutkowski

Abstract

We study generalized backward stochastic differential equations (BSDEs) up to a random time horizon $\vartheta$, which is not a stopping time, under minimal assumptions regarding the properties of $\vartheta$. In contrast to existing works in this area, we do not impose specific assumptions on the random time $\vartheta$ and we study the existence of solutions to BSDEs and reflected BSDEs with a random time horizon through the method of reduction. In addition, we also examine BSDEs and reflected BSDEs with a l\`adl\`ag driver where the driver is allowed to have a finite number of common jumps with the martingale part.

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  • Anna Aksamit & Libo Li & Marek Rutkowski, 2021. "Generalized BSDEs with random time horizon in a progressively enlarged filtration," Papers 2105.06654, arXiv.org.
    • Handle: RePEc:arx:papers:2105.06654
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    References listed on IDEAS

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    Cited by:

    1. Gapeev, Pavel V. & Li, Libo, 2022. "Perpetual American standard and lookback options with event risk and asymmetric information," LSE Research Online Documents on Economics 114940, London School of Economics and Political Science, LSE Library.

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