Related papers: Backward stochastic Volterra integral equations wi…

In this paper, we study backward stochastic differential equations driven by a G-Brownian motion. The solution of such new type of BSDE is a triple (Y,Z,K) where K is a decreasing G-martingale. Under a Lipschitz condition for generator f…

We address the optimal control of stochastic Volterra integral equations with delay through the lens of Hida-Malliavin calculus. We show that the corresponding adjoint processes satisfy an anticipated backward stochastic Volterra integral…

In [Stochastc Process. Appl., 122(9):3173-3208], the author proved the existence and the uniqueness of solutions to Markovian superquadratic BSDEs with an unbounded terminal condition when the generator and the terminal condition are…

In this paper, we study one-dimensional backward stochastic differential equation (BSDE, for short), whose coefficient $f$ is Lipschitz in $y$ but only continuous in $z$. In addition, if the terminal condition $\xi$ has bounded Malliavin…

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 consider a stochastic delay differential equation driven by a Holder continuous process and a Wiener process. Under fairly general assumptions on its coefficients, we prove that this equation is uniquely solvable. We also give sufficient…

The aim of this paper is to provide a comprehensive analysis of the path-dependent Stochastic Volterra Integral Equations (SVIEs), in which both the drift and the diffusion coefficients are allowed to depend on the whole trajectory of the…

The existence of strong solutions and pathwise uniqueness are established for one-dimensional stochastic Volterra equations with locally H{\"o}lder continuous diffusion coefficients and sufficiently regular kernels. Moreover, we study the…

Explicit solutions for a class of linear backward stochastic differential equations (BSDE) driven by Gaussian Volterra processes are given. These processes include the multifractional brownian motion and the multifractional…

In this paper, we discuss the solvability of backward stochastic differential equations (BSDEs) with superquadratic generators. We first prove that given a superquadratic generator, there exists a bounded terminal value, such that the…

The present paper is devoted to investigating the existence and uniqueness of solutions to a class of non-Lipschitz scalar valued backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs). In fact, when the…

Following our previous work [68], this paper continues to investigate the evolution dynamics of local times of spectrally positive L\'evy processes with Gaussian components in the spatial direction. We prove that conditioned on the…

In this paper, we investigate the inverse generator problem for abstract degenerate Volterra integro-differential equations in locally convex spaces. The classes of degenerate $(a,k)$-regularized $C$-resolvent families and degenerate mild…

We consider a class of stochastic control problems with a delayed control, both in drift and diffusion, of the type dX t = $\alpha$ t--d (bdt + $\sigma$dW t). We provide a new characterization of the solution in terms of a set of Riccati…

Path-dependence is a defining feature of many real-world systems, with applications ranging from population dynamics to rough volatility models and electricity spot prices. In stochastic Volterra equations (SVEs), such dependence is encoded…

In a noise driving by a multivariate point process $\mu$ with predictable compensator $\nu$, we prove existence and uniqueness of the reflected backward stochastic differential equation's solution with a lower obstacle…

For an $\cF_T$-measurable payoff of a European type contingent claim, the recursive utility process/dynamic risk measure can be described by the adapted solution to a backward stochastic differential equation (BSDE). However, for an…

We establish a general existence and uniqueness of integrable adapted solutions to scalar backward stochastic differential equations with integrable parameters, where the generator $g$ has an iterated-logarithmic uniform continuity in the…

We study the existence and uniqueness of the solution for the following backward stochastic variational inequality with oblique reflection (for short, $BSVI\left(H(t,y),\varphi,F\right)$), written under differential form \[…

In this paper, we introduce a class of backward stochastic equations (BSEs) that extend classical BSDEs and include many interesting examples of generalized BSDEs as well as semimartingale backward equations. We show that a BSE can be…