Related papers: Stochastic Volterra integral equations with jumps …

In this paper, we provide variation of constants formulae for linear (forward) stochastic Volterra integral equations (SVIEs, for short) and linear Type-II backward stochastic Volterra integral equations (BSVIEs, for short) in the usual…

Backward stochastic Volterra integral equations (BSVIEs in short) are studied. We introduce the notion of adapted symmetrical solutions (S-solutions in short), which are different from the M-solutions introduced by Yong [17]. We also give…

We study a class of stochastic integral equations with jumps under non-Lipschitz conditions. We use the method of Euler approximations to obtain the existence of the solution and give some sufficient conditions for the strong uniqueness.

We consider the explicit numerical approximations of stochastic differential equations (SDEs) driven by Brownian process and Poisson jump. It is well known that under non-global Lipschitz condition, Euler Explicit method fails to converge…

In the paper, we consider the no-explosion condition and pathwise uniqueness for SDEs driven by a Poisson random measure with coefficients that are super-linear and non-Lipschitz. We give a comparison theorem in the one-dimensional case…

Optimal control problems of forward stochastic Volterra integral equations (SVIEs) are formulated and studied. When control region is arbitrary subset of Euclidean space and control enters into the diffusion, necessary conditions of…

Backward stochastic differential equations (BSDEs) belong nowadays to the most frequently studied equations in stochastic analysis and computational stochastics. In this paper we prove that Picard iterations of BSDEs with globally Lipschitz…

We consider a stochastic volatility model with jumps where the underlying asset price is driven by the process sum of a 2-dimensional Brownian motion and a 2-dimensional compensated Poisson process. The market is incomplete, resulting in…

In this paper, we investigate the solvability of matrix valued Backward stochastic Riccati equations with jumps (BSREJ), which is associated with a stochastic linear quadratic (SLQ) optimal control problem with random coefficients and…

We study the existence and uniqueness of solutions to stochastic differential equations with Volterra processes driven by L\'evy noise. For this purpose, we study in detail smoothness properties of these processes. Special attention is…

We study stochastic equations of non-negative processes with jumps. The existence and uniqueness of strong solutions are established under Lipschitz and non-Lipschitz conditions. The comparison property of two solutions are proved under…

In this paper we study general nonlinear stochastic differential equations, where the usual Brownian motion is replaced by a L\'evy process. We also suppose that the coefficient multiplying the increments of this process is merely Lipschitz…

We consider a backward stochastic differential equation with jumps (BSDEJ) which is driven by a Brownian motion and a Poisson random measure. We present two candidate-approximations to this BSDEJ and we prove that the solution of each…

This paper adopts a highly effective numerical approach for approximating non-linear stochastic Volterra integral equations (NLSVIEs) based on the operational matrices of the Walsh function and the collocation method. The method transforms…

In this article we investigate the existence and uniqueness of the stochastic Volterra equation driven by a \levy noise of pure jump type. In particular, we consider the following type of equation $ du(t) = ( A\int_0 ^t b(t-s) u(s)\,ds) \,…

We consider the problem of the simulation of Levy-driven stochastic differential equations. It is generally impossible to simulate the increments of a Levy-process. Thus in addition to an Euler scheme, we have to simulate approximately…

For backward stochastic Volterra integral equations (BSVIEs) in multi-dimensional Euclidean spaces, comparison theorems are established in a systematic way for the adapted solutions and adapted M-solutions. For completeness, comparison…

For backward stochastic Volterra integral equations (BSVIEs, for short), under some mild conditions, the so-called adapted solutions or adapted M-solutions uniquely exist. However, satisfactory regularity of the solutions is difficult to…

In this paper, we consider parameter estimation for stochastic differential equations driven by Wiener processes and compound Poisson processes. We assume unknown parameters corresponding to coefficients of the drift term, diffusion term,…

In this note we prove an existence and uniqueness result of solution for stochastic Volterra integral equations driven by a fractional Brownian motion with Hurst parameter H > 1/2, showing also that the solution has finite moments. The…