Multivalued Backward Stochastic Differential Equations with Time Delayed Generators

Abstract

Our aim is to study the following new type of multivalued backward stochastic differential equation: \[ \left\{\begin{array} [c]{r}-dY\left(t\right) +\partialφ\left(Y\left(t\right)\right) dt\ni F\left(t,Y\left(t\right),Z\left(t\right),Y_{t},Z_{t}\right) dt+Z\left(t\right) dW\left(t\right),\;0\leq t\leq T,\medskip\\ \multicolumn{1}{l}{Y\left(T\right) =ξ,}\end{array} \right. \] where $\partial \phi$ is the subdifferential of a convex function and $\left(Y_t,Z_t\right):=(Y(t+\theta ),Z(t+\theta ){)}_{\theta \in [-T,0]}$ represent the past values of the solution over the interval $\left[0,t\right]$. Our results are based on the existence theorem from Delong & Imkeller, Ann. Appl. Probab., 2010, concerning backward stochastic differential equations with time delayed generators.

14 pages

References in corpus (4)

• Backward stochastic variational inequalities on random interval
• Applications of time-delayed backward stochastic differential equations to pricing, hedging and portfolio management
• Numerical Schemes for Multivalued Backward Stochastic Differential Systems
• On Malliavin's differentiability of BSDE with time delayed generators driven by Brownian motions and Poisson random measures

Cited by in corpus (2)

• Backward stochastic variational inequalities on random interval
• Multivalued backward doubly stochastic differential equations with time delayed coefficients