Backward Stochastic Volterra Integral Equations With Non-Lipschitz Time Delayed Generators

Reflected backward doubly stochastic differential equations with time delayed generators

We consider a class of reflected backward doubly stochastic differential equations with time delayed generator (in short RBDSDE with time delayed generator), in this case generator at time t can depend on the values of a solution in the past. Under a Lipschitz condition, we ensure the existence and uniqueness of the solution.

Mean-Field Backward Stochastic Volterra Integral Equations

Mean-field backward stochastic Volterra integral equations (MF-BSVIEs, for short) are introduced and studied. Well-posedness of MF-BSVIEs in the sense of introduced adapted Msolutions is established. Two duality principles between linear mean-field (forward) stochastic Volterra integral equations (MF-FSVIEs, for short) and MF-BSVIEs are obtained. Several comparison theorems for MF-FSVIEs and MF...

Stochastic Volterra integral equations with a parameter

Optimal Control Problems of Forward-Backward Stochastic Volterra Integral Equations with Closed Control Regions

Abstract. Optimal control problems of forward-backward stochastic Volterra integral equations (FBSVIEs, in short) with closed control regions are formulated and studied. Instead of using spike variation method as one may imagine, here we turn to treat the non-convexity of the control regions by borrowing some tools in set-valued analysis and adapting them into our stochastic control systems. A ...

Dissipative backward stochastic differential equations with locally Lipschitz nonlinearity

In this paper we study a class of backward stochastic differential equations (BSDEs) of the form dYt = −AYtdt−f0(t, Yt)dt−f1(t, Yt, Zt)dt+ZtdWt, 0 ≤ t ≤ T ; YT = ξ in an infinite dimensional Hilbert space H , where the unbounded operator A is sectorial and dissipative and the nonlinearity f0(t, y) is dissipative and defined for y only taking values in a subspace of H . A typical example is prov...