Switching problem and related system of reflected backward SDEs

BSDE representations for optimal switching problems with controlled volatility

“…Under (H1) and (H2), Theorem 4.2 in [10] provides the existence of a unique solution to (4.1), for any parameter (ν, η) ∈ K, and we denote by O ν,.,η the corresponding frontier for the domain of Y ν,.,η defined by…”

A note on existence and uniqueness for solutions of multidimensional reflected BSDEs

“…Since (H3) is stronger than (H2), the existence of a solution is provided by Theorem 3.2 in [3]. Due to the the particular form of switching oblique reflections and for sake of completeness, we decide to report here a simplified sketch of proof.…”

“…Recently, Hu and Tang [4] introduced and studied a new type of BSDE, constrained by oblique reflections, and associated to optimal switching problems. Via heavy arguments, Hamadène and Zhang [3] generalized the form of these multidimensional reflected BSDEs. They allow for the consideration of more general oblique constraints, as well as drivers depending on the global solution of the BSDE.…”

“…As in [4] or [3] in a more general framework, this assumption makes instantaneous switching irrelevant. We introduce the family of random closed convex sets (C t ) 0≤t≤T associated to C:…”

Optimal switching problems under partial information

“…For these connections, and the application of multi-mode optimal switching problems to economics and mathematics, see [AH09], [DH09], [DHP10], [HM12], [HT07], [PVZ09], [LNO12] and the references therein. More on reflected backward stochastic differential equations in the context of optimal switching problems can be found in [AF12], [DH09], [DHP10], [HT07] and [HZ10].…”