2023/09/10 by Joshua Zoen-Git Hiew, Tongseok Lim, Hiew, Joshua Zoen-Git +5
Economics, Econometrics and Finance · Mathematics · #Applied mathematics #Climate Change Policy and Economics #Computer science #Dimension (graph theory) #Economic theories and models #Economics #FOS: Economics and business #FOS: Mathematics #Martingale (probability theory) #Mathematical Finance (q-fin.MF) #Mathematical analysis #Mathematical economics #Mathematical optimization #Mathematics #Modular design #Monotonic function #Optimization and Control (math.OC) #Probability (math.PR) #Pure mathematics #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2309.04947
openalex publication_date 2023/09/10 · openalex created_date 2023/09/13 · openalex updated_date 2026/07/28
This paper addresses the problem of robust option pricing within the framework of Vectorial Martingale Optimal Transport (VMOT). We investigate the geometry of VMOT solutions for N-period market models and demonstrate that, when the number of underlying assets is d=2 and the payoff is sub- or supermodular, the extremal model reduces to a single-factor structure in the first period. This structural result allows for a significant dimension reduction, transforming the problem into a more tractable format. We prove that this reduction is specific to the two-asset case and provide counterexamples showing it generally fails for d ≥ 3. Finally, we exploit this monotonicity to develop a reduced-dimension Sinkhorn algorithm. Numerical experiments demonstrate that this structure-preserving approach reduces computational time by approximately 99% compared to standard methods while improving accuracy.