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

Christian Bender; Lauri Viitasaari

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arXiv · 1509.02257

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

Christian Bender·Lauri Viitasaari

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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 $H\in (0,1)\setminus \{\frac12\}$. We show that, for every choice of deterministic coefficient functions, there is a square integrable terminal condition such that the equation has no solution.

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Christian Bender, Lauri Viitasaari. 2015-09-08. A general non-existence result for linear BSDEs driven by Gaussian processes. https://arxiv.org/abs/1509.02257

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