2020/03/13 by Ghoussoub, Nassif, Kim, Young-Heon, Palmer, Aaron Zeff
#60 #FOS: Mathematics #Optimization and Control (math.OC) #Primary 49 #Probability (math.PR) #secondary 52
paper · doi:10.48550/arxiv.2003.06465
Given a stochastic state process (Xt)t and a real-valued submartingale cost process (St)t, we characterize optimal stopping times τ that minimize the expectation of Sτ while realizing given initial and target distributions μ and ν, i.e., X0∼ μ and Xτ∼ ν. A dual optimization problem is considered and shown to be attained under suitable conditions. The optimal solution of the dual problem then provides a contact set, which characterizes the location where optimal stopping can occur. The optimal stopping time is uniquely determined as the first hitting time of this contact set provided we assume a natural structural assumption on the pair (Xt, St)t, which generalizes the twist condition on the cost in optimal transport theory. This paper extends the Brownian motion settings studied in [15, 16] and deals with more general costs.