Backward stochastic differential equations with constraints on the gains-process

Backward Stochastic Differential Equations with Constraints on the Gains - Process

We consider backward stochastic differential equations with convex constraints on the gains (or intensity-of-noise) process. Existence and uniqueness of a minimal solution are established in the case of a drift coefficient which is Lipschitz continuous in the state and gains processes and convex in the gains process. It is also shown that the minimal solution can be characterized as the unique ...

Backward Stochastic Diierential Equations with Constraints on the Gains-process

We consider Backward Stochastic Diierential Equations with convex constraints on the gains (or intensity-of-noise) process. Existence and uniqueness of a minimal solution are established in the case of a drift coeecient which is Lipschitz-continuous in the state-and gains-processes, and convex in the gains-process. It is also shown that the minimal solution can be characterized as the unique so...

Backward Stochastic Differential Equations on Manifolds

The problem of finding a martingale on a manifold with a fixed random terminal value can be solved by considering BSDEs with a generator with quadratic growth. We study here a generalization of these equations and we give uniqueness and existence results in two different frameworks, using differential geometry tools. Applications to PDEs are given, including a certain class of Dirichlet problem...

Backward Stochastic Differential Equations on Manifolds II

In [1], we have studied a generalization of the problem of finding a martingale on a manifold whose terminal value is known. This article completes the results obtained in the first article by providing uniqueness and existence theorems in a general framework (in particular if positive curvatures are allowed), still using differential geometry tools.

On Solving Backward Doubly Stochastic Differential Equations