Switching game of backward stochastic differential equations and associated system of obliquely reflected backward stochastic differential equations

Ying  Hu; Shanjian  Tang

doi:10.3934/dcds.2015.35.5447

Article Contents

2015, Volume 35, Issue 11: 5447-5465. Doi: 10.3934/dcds.2015.35.5447

This issue Previous Article Some linear-quadratic stochastic differential games for equations in Hilbert spaces with fractional Brownian motions Next Article A Dynkin game under Knightian uncertainty

Switching game of backward stochastic differential equations and associated system of obliquely reflected backward stochastic differential equations

Ying Hu^1, and
Shanjian Tang^2,

1.
IRMAR, Université Rennes 1, Campus de Beaulieu, F-35042 Rennes Cedex
2.
School of Mathematical Science, Fudan University, Shanghai 200433

Received: November 2013

Revised: November 2014

Published: November 2015

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Abstract

This paper is concerned with the switching game of a one-dimensional backward stochastic differential equation (BSDE). The associated Bellman-Isaacs equation is a system of matrix-valued BSDEs living in a special unbounded convex domain with reflection on the boundary along an oblique direction. In this paper, we show the existence of an adapted solution to this system of BSDEs with oblique reflection by the penalization method, the monotone convergence, and the a priori estimates.

Keywords:

Switching game,
backward stochastic differential equations,
oblique reflection.

Mathematics Subject Classification: 93E20, 93E03, 49L20, 34F05, 60H10.

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