2018/12/09 by Ivan Guo, Guo, Ivan, Grégoire Loeper +2 · 3 citations
Economics, Econometrics and Finance · Mathematics · #Applied mathematics #Calibration #Climate Change Policy and Economics #Computer science #Dimension (graph theory) #Duality (order theory) #Econometrics #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Local volatility #Mathematical Finance (q-fin.MF) #Mathematical analysis #Mathematical optimization #Mathematics #Optimization and Control (math.OC) #Partial differential equation #Path (computing) #Path dependent #Probability (math.PR) #Pure mathematics #Semimartingale #Stochastic processes and financial applications #Stochastic volatility #Volatility (finance) #math.OC #math.PR #q-fin.MF
paper · pdf · doi:10.48550/arxiv.1812.03526
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2018/12/09 · arxiv created 2020/09/13 · arxiv updated 2020/09/15 · openalex created_date 2021/02/01 · openalex updated_date 2026/08/05
In this paper, we introduce and develop the theory of semimartingale optimal\ntransport in a path dependent setting. Instead of the classical constraints on\nmarginal distributions, we consider a general framework of path dependent\nconstraints. Duality results are established, representing the solution in\nterms of path dependent partial differential equations (PPDEs). Moreover, we\nprovide a dimension reduction result based on the new notion of\n"semifiltrations", which identifies appropriate Markovian state variables based\non the constraints and the cost function. Our technique is then applied to the\nexact calibration of volatility models to the prices of general path dependent\nderivatives.\n