Related papers: On path-dependent multidimensional forward-backwar…
We study a class of backward stochastic differential equations (BSDEs) driven by a random measure or, equivalently, by a marked point process. Under appropriate assumptions we prove well-posedness and continuous dependence of the solution…
This work concerns the dynamics of a certain class of delay differential equations (DDEs) which we refer to as state dependent delay maps. These maps are generated by delay differential equations where the derivative of the current state…
This paper studies path stabilities of the solution to stochastic differential equations (SDE) driven by time-changed L\'evy noise. The conditions for the solution of time-changed SDE to be path stable and exponentially path stable are…
In this paper, we introduce a type of path-dependent quasilinear (parabolic) partial differential equations in which the (continuous) paths on an interval [0,t] becomes the basic variables in the place of classical variables (t,x). This new…
In this paper, a Banach space framework is introduced in order to deal with finite-dimensional path-dependent stochastic differential equations. A version of Kolmogorov backward equation is formulated and solved both in the space of $L^p$…
We study linear-quadratic stochastic optimal control problems with bilinear state dependence for which the underlying stochastic differential equation (SDE) consists of slow and fast degrees of freedom. We show that, in the same way in…
We define fully coupled forward-backward stochastic differential equations on spaces related to continuous time, finite state Markov Chains. Existence and uniqueness results of the fully coupled forward-backward stochastic differential…
We establish an existence and uniqueness result for a class of multidimensional quadratic backward stochastic differential equations (BSDE). This class is characterized by constraints on some uniform a priori estimate on solutions of a…
The present paper is devoted to the study of the well-posedness of a type of BSDEs with triangularly quadratic generators. This work is motivated by the recent results obtained by Hu and Tang [14] and Xing and \v{Z}itkovi\'{c} [28]. By the…
We provide an extension of the unbiased simulation method for SDEs developed in Henry-Labordere et al. [Ann Appl Probab. 27:6 (2017) 1-37] to a class of path-dependent dynamics, pertaining for Asian options. In our setting, both the payoff…
We consider stochastic differential equations on $\mathbb R^d$ with coefficients depending on the path and distribution for the whole history. Under a local integrability condition on the time-spatial singular drift, the well-posedness and…
We address a general optimal switching problem over finite horizon for a stochastic system described by a differential equation driven by Brownian motion. The main novelty is the fact that we allow for infinitely many modes (or regimes,…
This paper studies a class of non$-$Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a $Z-$constrained…
We establish existence and uniqueness of minimax solutions for a fairly general class of path-dependent Hamilton-Jacobi equations. In particular, the relevant Hamiltonians can contain the solution and they only need to be measurable with…
Forward-backward stochastic differential equations (FBSDEs) have been generalized by introducing jumps for better capturing random phenomena, while the resulting FBSDEs are far more intricate than the standard one from every perspective. In…
In this paper, we consider a stochastic decision problem for a system governed by a stochastic differential equation, in which an optimal decision is made in such a way to minimize a vector-valued accumulated cost over a finite-time horizon…
We extend stochastic basis adaptation and spatial domain decomposition methods to solve time varying stochastic partial differential equations (SPDEs) with a large number of input random parameters. Stochastic basis adaptation allows the…
For a backward stochastic differential equation (BSDE, for short), when the generator is not progressively measurable, it might not admit adapted solutions, shown by an example. However, for backward stochastic Volterra integral equations…
In this paper, we study the multi-dimensional backward stochastic differential equations (BSDEs) whose generator depends also on the mean of both variables. When the generator is diagonally quadratic, we prove that the BSDE admits a unique…
Motivated by the idea of imposing paralleling computing on solving stochastic differential equations (SDEs), we introduce a new Domain Decomposition Scheme to solve forward-backward stochastic differential equations (FBSDEs) parallely. We…