We solve the Skorokhod embedding problem for a class of stochastic processes satisfying an inhomogeneous stochastic differential equation (SDE) of the form dAt = μ(t,At)dt + σ(t,At)dWt. We provide sufficient conditions guaranteeing that for a given probability measure ν on R there exists a bounded stopping time τ and a real a such that the solution (At) of the SDE with initial value a satisfies Aτ ∼ ν. We hereby distinguish the cases where (At) is a solution of the SDE in a weak or strong sense. Our construction of embedding stopping times is based on a solution of a fully coupled forward-backward SDE. We use the so-called method of decoupling fields for verifying that the FBSDE has a unique solution. Finally, we sketch an algorithm for putting our theoretical construction into practice and illustrate it with a numerical experiment.
|Number of pages
|Annales de l'institut Henri Poincare (B) Probability and Statistics
|Published - Aug 2020
- Decoupling fields
- Skorokhod embedding