Stochastic transforms for jump diffusion processes combined with related backward stochastic differential equations

Stabilized Numerical Methods for Stochastic Differential Equations driven by Diffusion and Jump-Diffusion Processes

Stochastic models that account for sudden, unforeseeable events play a crucial role in many different fields such as finance, economics, biology, chemistry, physics and so on. That kind of stochastic problems can be modeled by stochastic differential equations driven by jumpdiffusion processes. In addition, there are situations, where a stochastic model is based on stochastic differential equat...

Anticipated Backward Stochastic Differential Equations

In this paper, we discuss a new type of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also the future. We show that these anticipated BSDEs have unique solutions, a comparison theorem for their solutions, and a duality between them and ...

Fast Communication Two-stage Stochastic Runge-kutta Methods for Stochastic Differential Equations with Jump Diffusion

Backward stochastic differential equations with Young drift

We show the well-posedness of backward stochastic differential equations containing an additional drift driven by a path of finite q-variation with q ∈ [1, 2). In contrast to previous work, we apply a direct fixpoint argument and do not rely on any type of flow decomposition. The resulting object is an effective tool to study semilinear rough partial differential equations via a Feynman–Kac typ...

Backward Stochastic Differential Equations with Stochastic Monotone Coefficients

We prove an existence and uniqueness result for backward stochastic differential equations whose coefficients satisfy a stochastic monotonicity condition. In this setting, we deal with both constant and random terminal times. In the random case, the terminal time is allowed to take infinite values. But in aMarkovian framework, that is coupled with a forward SDE, our result provides a probabilis...