scholarly journals A probabilistic verification theorem for the finite horizon two-player zero-sum optimal switching game in continuous time

2019 ◽  
Vol 51 (2) ◽  
pp. 425-442
Author(s):  
S. Hamadène ◽  
R. Martyr ◽  
J. Moriarty
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Continuous Time ◽  
Backward Stochastic Differential Equations ◽  
Finite Horizon ◽  
Optimal Switching ◽  
Verification Theorem ◽  
A Value ◽  
Zero Sum ◽  
Switching Game

AbstractIn this paper we study continuous-time two-player zero-sum optimal switching games on a finite horizon. Using the theory of doubly reflected backward stochastic differential equations with interconnected barriers, we show that this game has a value and an equilibrium in the players’ switching controls.

scholarly journals Systems of BSDES with oblique reflection and related optimal switching problems

2019 ◽  
Vol 19 (04) ◽  
pp. 1950030
Author(s):  
Mateusz Topolewski
Keyword(s):  
Continuous Function ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Backward Stochastic Differential Equations ◽  
Type Condition ◽  
Optimal Switching ◽  
Existence Of A Solution ◽  
Oblique Reflection ◽  
Probability Spaces

We consider systems of backward stochastic differential equations with càdlàg upper barrier [Formula: see text] and oblique reflection from below driven by an increasing continuous function [Formula: see text]. Our equations are defined on general probability spaces with a filtration satisfying merely the usual assumptions of right continuity and completeness. We assume that the pair [Formula: see text] satisfies a Mokobodzki-type condition. We prove the existence of a solution for integrable terminal conditions and integrable quasi-monotone generators. Applications to the optimal switching problem are given.

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