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

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 $H\in (0,1)\setminus \{\frac{1}{2}\}$. We show that, for every choice of deterministic coefficient functions, there is a square integrable terminal condition such that the equation has no solution.