2016/11/08 by Beatrice Acciaio, Julio Backhoff‐Veraguas, Julio Backhoff Veraguas +4 · 5 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60G44 #90C08 #91G80 #Applied mathematics #Brownian motion #Computer science #Context (archaeology) #Diffusion process #Economic theories and models #FOS: Mathematics #Filtration (mathematics) #Geometric Brownian motion #Martingale (probability theory) #Mathematical optimization #Mathematics #Minification #Optimal stopping #Optimization and Control (math.OC) #Probability (math.PR) #Pure mathematics #Risk and Portfolio Optimization #Semimartingale #Statistics #Stochastic processes and financial applications #math.OC #math.PR #msc:60G44 #msc:90C08 #msc:91G80
paper · pdf · doi:10.48550/arxiv.1611.02610
published in arXiv (Cornell University) (Cornell University) · 33 pages
openalex publication_date 2016/11/08 · arxiv created 2017/12/12 · arxiv updated 2017/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The martingale part in the semimartingale decomposition of a Brownian motion\nwith respect to an enlargement of its filtration, is an anticipative mapping of\nthe given Brownian motion. In analogy to optimal transport theory, we define\ncausal transport plans in the context of enlargement of filtrations, as the\nKantorovich counterparts of the aforementioned non-adapted mappings. We provide\na necessary and sufficient condition for a Brownian motion to remain a\nsemimartingale in an enlarged filtration, in terms of certain minimization\nproblems over sets of causal transport plans. The latter are also used in order\nto give robust transport-based estimates for the value of having additional\ninformation, as well as model sensitivity with respect to the reference\nmeasure, for the classical stochastic optimization problems of utility\nmaximization and optimal stopping. Our results have natural extensions to the\ncase of general multidimensional continuous semimartingales.\n