2022/03/11 by Andrea Bovo, Bovo, Andrea, Tiziano De Angelis +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #35K58 #49J40 #60G40 #91A05 #91A15 #93E20 #Analysis of PDEs (math.AP) #Climate Change Policy and Economics #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2203.06247
openalex publication_date 2022/03/11 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
We study a class of zero-sum games between a singular-controller and a\nstopper over finite-time horizon. The underlying process is a multi-dimensional\n(locally non-degenerate) controlled stochastic differential equation (SDE)\nevolving in an unbounded domain. We prove that such games admit a value and\nprovide an optimal strategy for the stopper. The value of the game is shown to\nbe the maximal solution, in a suitable Sobolev class, of a variational\ninequality of `min-max' type with obstacle constraint and gradient constraint.\nAlthough the variational inequality and the game are solved on an unbounded\ndomain we do not require boundedness of either the coefficients of the\ncontrolled SDE or of the cost functions in the game.\n