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

Lubomir Banas, Giorgio Ferrari and Tsiry Avisoa Randrianasolo
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Lubomir Banas: Center for Mathematical Economics, Bielefeld University
Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University
Tsiry Avisoa Randrianasolo: Center for Mathematical Economics, Bielefeld University

No 630, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: 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 w.r.t. the time and convexity variables, and show that the scheme converges to the unique viscosity solution of the considered problem. Furthermore, we generalize the semi-discrete 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.

Keywords: zero-sum stochastic differential games; asymmetric information; probabilistic numerical approximation; discrete convex envelope; convexity constrained Hamilton-Jacobi- Bellmann equation; viscosity solution (search for similar items in EconPapers)
Pages: 28
Date: 2020-01-13
New Economics Papers: this item is included in nep-gth
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https://pub.uni-bielefeld.de/download/2939974/2939975 First Version, 2019 (application/pdf)

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