2024/01/22 by Daniel Kršek, Kršek, Daniel, Gudmund Pammer +1 · 1 citation
Economics, Econometrics and Finance · #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Fiscal Policy and Economic Growth #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2401.11958
openalex publication_date 2024/01/22 · openalex created_date 2024/01/24 · openalex updated_date 2026/07/28
We investigate duality and existence of dual optimizers for several adapted optimal transport problems under minimal assumptions. This includes the causal and bicausal transport, the causal and bicausal barycenter problem, and a multimarginal problem incorporating causality constraints. Moreover, we characterize polar sets in the causal and bicausal setting and discuss applications of our results in robust finance. We consider a non-dominated model of several financial markets where stocks are traded dynamically, but the joint stock dynamics are unknown. We show that a no-arbitrage assumption naturally leads to sets of multicausal couplings. Consequently, computing the robust superhedging price is equivalent to solving an adapted transport problem, and finding a superhedging strategy means solving the corresponding dual.