## Abstract

We solve the Skorokhod embedding problem for a class of stochastic processes satisfying an inhomogeneous stochastic differential equation (SDE) of the form dA_{t} = μ(t,A_{t})dt + σ(t,A_{t})dW_{t}. 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 (A_{t}) of the SDE with initial value a satisfies A_{τ} ∼ ν. We hereby distinguish the cases where (A_{t}) 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.

Original language | English |
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Pages (from-to) | 1606-1640 |

Number of pages | 35 |

Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |

Volume | 56 |

Issue number | 3 |

DOIs | |

Publication status | Published - Aug 2020 |

## Keywords

- Decoupling fields
- FBSDE
- Skorokhod embedding