Related papers: On the stochastic decision problems with backward …
In this paper, we study the doubly conditional reflected backward stochastic differential equations (BSDEs), where constraints are made on the conditional expectation of the first component of the solution with respect to a general…
We consider a class of backward stochastic differential equations (BSDEs) driven by Brownian motion and Poisson random measure, and subject to constraints on the jump component. We prove the existence and uniqueness of the minimal solution…
In this paper, we study a kind of constrained backward stochastic differential equations (BSDEs) such that the nonlinear expectation of the composition of a loss function and the solution remains above zero. The existence and uniqueness…
In this paper, we study a stochastic recursive optimal control problem in which the system is governed by a functional forward-backward stochastic differential equation. Under standard assumptions, we establish the dynamic programming…
In this paper, we study reflected backward stochastic difference equations (RBSDEs for short) with finitely many states in discrete time. The general existence and uniqueness result, as well as comparison theorems for the solutions, are…
We study a stochastic optimal control problem for forward-backward control systems with quadratic generators. In order to establish the first and second-order variational and adjoint equations, we obtain a new estimate for one-dimensional…
We study a stochastic optimal control problem for fully coupled forward-backward stochastic control systems with a nonempty control domain. For our problem, the first-order and second-order variational equations are fully coupled linear…
We investigate the optimal reinsurance problem under the criterion of maximizing the expected utility of terminal wealth when the insurance company has restricted information on the loss process. We propose a risk model with claim arrival…
We consider an infinite horizon, obliquely reflected backward stochastic differential equation (RBSDE). The main contribution of the present work is that we generalize previous results on infinite horizon reflected BSDEs to the setting…
We study the optimal liquidation problems in target zone models using dynamic programming methods. Such control problems allow for stochastic differential equations with reflections and random coefficients. The value function is…
We propose the Compound BSDE method, a fully forward, deep-learning-based approach for solving a broad class of problems in financial mathematics, including optimal stopping. The method is based on a reformulation of option pricing problems…
This paper deals with the long time behavior of the optimal solution of stochastic backward linear-quadratic optimal control problem over the finite time horizon. Both weak and strong turnpike properties are established under appropriate…
In this paper we study the optimal stochastic control problem for a path-dependent stochastic system under a recursive path-dependent cost functional, whose associated Bellman equation from dynamic programming principle is a path-dependent…
This paper addresses the optimal covariance steering problem for stochastic discrete-time linear systems subject to probabilistic state and control constraints. A method is presented for efficiently attaining the exact solution of the…
Motivated from time-inconsistent stochastic control problems, we introduce a new type of coupled forward-backward stochastic systems, namely, flows of forward-backward stochastic differential equations. They are systems consisting of a…
In this paper, we address the problem of existence and uniqueness of a global classical solution to a multidimensional stochastic Burgers equation without gradient-type assumptions on the force or the initial condition. The equation is…
This paper addresses the numerical solution of backward stochastic differential equations (BSDEs) arising in stochastic optimal control. Specifically, we investigate two BSDEs: one derived from the Hamilton-Jacobi-Bellman equation and the…
We prove results on bounded solutions to backward stochastic equations driven by random measures. Those bounded BSDE solutions are then applied to solve different stochastic optimization problems with exponential utility in models where the…
We establish the existence of both optimal relaxed controls and strict optimal controls for systems driven by Reflected Stochastic Differential Equations RSDEs. Our approach is based on weak convergence techniques for the associated RSDEs…
The present paper is devoted to the study of diagonally quadratic backward stochastic differential equation with oblique reflection. Using a penalization approach, we show the existence fo a solution by providing some delicated a priori…