Related papers: Multi-Dimensional Super-Linear Backward Stochastic…
The problem of finding a martingale on a manifold with a fixed random terminal value can be solved by considering BSDEs with a generator with quadratic growth. We study here a generalization of these equations and we give uniqueness and…
This paper is concerned with an optimal control problem for a forward-backward stochastic differential equation (FBSDE, for short) with a recursive cost functional determined by a backward stochastic Volterra integral equation (BSVIE, for…
In this paper stochastic Volterra equations admitting exponentially bounded resolvents are studied. After obtaining convergence of resolvents, some properties of stochastic convolutions are given. The paper provides a sufficient condition…
In this paper, we study multi-dimensional reflected backward stochastic differential equations with diagonally quadratic generators. Using the comparison theorem for diagonally quadratic BSDEs which is established recently in [14], we…
In this paper, we study the doubly reflected backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs for short) when the generator has quadratic growth in the $z$-component. Based on the theory of $G$-BMO…
The present paper is devoted to study multi-dimensional coupled FBSDEs with diagonally quadratic generators. Relying on a comparison result obtained in [20], we provide conditions under which there exists a global solution. As a byproduct,…
We give local and global existence and uniqueness results for systems of coupled FBSDEs in the multidimensional setting and with generators allowed to grow arbitrarily fast in the control variable. Our results are based on Malliavin…
In this paper, the theory of mean-field backward doubly stochastic Volterra integral equations (MF-BDSVIEs) is studied. First, we derive the well-posedness of M-solutions to MFBDSVIEs, and prove the comparison theorem for such a type of…
In this paper we consider unbounded solutions of perturbed convolution Volterra summation equations. The equations studied are asymptotically sublinear, in the sense that the state--dependence in the summation is of smaller than linear…
We investigate the continuous-time Markowitz mean-variance portfolio selection problem within a multivariate class of fake stationary affine Volterra models. In this non-Markovian and non-semimartingale market framework with unbounded…
This article deals with the numerical approximation of Markovian backward stochastic differential equations (BSDEs) with generators of quadratic growth with respect to $z$ and bounded terminal conditions. We first study a slight…
We study the problem of existence of solutions for generalized backward stochastic differential equation with two reflecting barriers (GRBSDE for short) under weaker assumptions on the data. Roughly speaking we show the existence of a…
We consider a Backward Stochastic Differential Equation (BSDE for short) in a Markovian framework for the pair of processes $(Y,Z)$, with generator with quadratic growth with respect to $Z$. The forward equation is an evolution equation in…
In this article we study the existence and the uniqueness of a solution for reflected backward stochastic differential equations in the case when the generator is logarithmic growth in the $z$-variable $(|z|\sqrt{|\ln(|z|)|})$, the terminal…
In this paper, we generalize to Gaussian Volterra processes the existence and uniqueness of solutions for a class of non linear backward stochastic differential equations (BSDE) and we establish the relation between the non linear BSDE and…
In this paper, we study the multi-dimensional reflected backward stochastic differential equation driven by $G$-Brownian motion ($G$-BSDE) with a multi-variate constraint on the $G$-expectation of its solution. The generators are diagonally…
This paper is dedicated to the analysis of forward backward stochastic differential equations driven by a L{\'e}vy process. We assume that the generator and the terminal condition are path-dependent and satisfy a local Lipschitz condition.…
Variational autoencoders (VAE) represent a popular, flexible form of deep generative model that can be stochastically fit to samples from a given random process using an information-theoretic variational bound on the true underlying…
This paper concerns the finite-time blow-up and asymptotic behaviour of solutions to nonlinear Volterra integrodifferential equations. Our main contribution is to determine sharp estimates on the growth rates of both explosive and…
A Backward Stochastic Differential Equation (BSDE) with a Peano-type generator, is known to have infinitely many solutions when the terminal value is vanishing, and is shown to have possibly multiple solutions even when the terminal value…