2014/03/10 by David Hobson, Hobson, David
Computer Science · Economics, Econometrics and Finance · Mathematics · #60G40 #60G44 #60J60 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60G40 #msc:60G44 #msc:60J60
paper · pdf · doi:10.48550/arxiv.1403.2214
arxiv created 2014/03/10 · openalex publication_date 2014/03/10 · arxiv updated 2014/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Suppose X is a time-homogeneous diffusion on an interval IX ⊆ \mathbb R and let μ be a probability measure on IX. Then τ is a solution of the Skorokhod embedding problem (SEP) for μ in X if τ is a stopping time and Xτ∼ μ. There are well-known conditions which determine whether there exists a solution of the SEP for μ in X. We give necessary and sufficient conditions for there to exist an integrable solution. Further, if there exists a solution of the SEP then there exists a minimal solution. We show that every minimal solution of the SEP has the same first moment. When X is Brownian motion, every integrable embedding of μ is minimal. However, for a general diffusion there may be integrable embeddings which are not minimal.