2014/02/18 by Mihai Ŝırbu, Sîrbu, Mihai
Economics, Econometrics and Finance · Mathematics · #Economic theories and models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Optimization and Control (math.OC) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1402.4415
openalex publication_date 2014/02/18 · openalex created_date 2022/08/08 · openalex updated_date 2026/07/28
We consider a Markovian stochastic control problem with model uncertainty.\nThe controller (intelligent player) observes only the state, and, therefore,\nuses feed-back (closed-loop) strategies. The adverse player (nature) who does\nnot have a direct interest in the pay-off, chooses open-loop controls that\nparametrize Knightian uncertainty. This creates a two-step optimization problem\n(like half of a game) over feed-back strategies and open-loop controls. The\nmain result is to show that, under some assumptions, this provides the same\nvalue as the (half of) the zero-sum symmetric game where the adverse player\nalso plays feed-back strategies and actively tries to minimize the pay-off. The\nvalue function is independent of the filtration accessible to the adverse\nplayer. Aside from the modeling issue, the present note is a technical\ncompanion to [S I3b].\n