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

Publikationen: Beitrag in FachzeitschriftArtikelForschung(peer-reviewed)

Autoren

Externe Organisationseinheiten

  • Universität Bielefeld

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 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.

Details

OriginalspracheEnglisch
Seiten (von - bis)1109–1135
Seitenumfang27
FachzeitschriftSIAM journal on control and optimization
Jahrgang59.2021
Ausgabenummer2
Frühes Online-Datum24 März 2021
DOIs
StatusVeröffentlicht - 2021