BSDE representations for optimal switching problems with controlled volatility.

Summary This paper provides two different strong BSDE representations for optimal switching problems in the case where the dynamics of the underlying diffusion process depends on the current value of the switching mode. These new representations are valid in a non-Markovian framework and make use of either one-dimensional constrained BS-DEs with jumps or multidimensional BSDEs with oblique reflections, thus extending the framework considered by Hu and Tang [12]. In particular, the numerical resolu-tion of the corresponding switching problem can therefore be treated via the entirely probabilistic schemes presented in [4] or [8].