Numerical Approximation of the Value of a Stochastic Differential Game with Asymmetric Information

Ľubomír Baňas, Giorgio Ferrari, Tsiry Avisoa Randrianasolo

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We consider a convexity constrained Hamilton--Jacobi--Bellman-type obstacle problem for the value function of a zero-sum differential game with asymmetric information. We propose a convexity-preserving probabilistic numerical scheme for the approximation of the value function which is discrete with respect to the time and convexity variables, and we show that the scheme converges to the unique viscosity solution of the considered problem. Furthermore, we generalize the semidiscrete scheme to obtain an implementable fully discrete numerical approximation of the value function and present numerical experiments to demonstrate the properties of the proposed numerical scheme.
Original languageEnglish
Pages (from-to)1109–1135
Number of pages27
JournalSIAM journal on control and optimization
Issue number2
Early online date24 Mar 2021
Publication statusPublished - 2021

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