Related papers: Value Function Estimators for Feynman-Kac Forward-…
In this paper, a singular value decomposition (SVD) approach is developed for implementing the cubature Kalman filter. The discussed estimator is one of the most popular and widely used method for solving nonlinear Bayesian filtering…
This paper is mainly concerned with the solutions to both forward and backward mean-field stochastic partial differential equation and the corresponding optimal control problem for mean-field stochastic partial differential equation. We…
In this paper, we study policy evaluation in continuous-time reinforcement learning (RL), where the state follows an unknown stochastic differential equation (SDE), but only discrete-time data are available. We first highlight that the…
In this paper, we consider optimal control of stochastic differential equations subject to an expected path constraint. The stochastic maximum principle is given for a general optimal stochastic control in terms of constrained FBSDEs. In…
Recent results in the study of the Hamilton Jacobi Bellman (HJB) equation have led to the discovery of a formulation of the value function as a linear Partial Differential Equation (PDE) for stochastic nonlinear systems with a mild…
Optimal control problem is typically solved by first finding the value function through Hamilton-Jacobi equation (HJE) and then taking the minimizer of the Hamiltonian to obtain the control. In this work, instead of focusing on the value…
In this paper, we propose forward and backward stochastic differential equations (FBSDEs) based deep neural network (DNN) learning algorithms for the solution of high dimensional quasilinear parabolic partial differential equations (PDEs),…
We consider policy evaluation in infinite-horizon discounted Markov decision problems (MDPs) with infinite spaces. We reformulate this task a compositional stochastic program with a function-valued decision variable that belongs to a…
We a controlled system driven by a coupled forward-backward stochastic differential equation (FBSDE) with a non degenerate diffusion matrix. The cost functional is defined by the solution of the controlled backward stochastic differential…
We extend the wellposedness results for second order backward stochastic differential equations introduced by Soner, Touzi and Zhang \cite{stz} to the case of a bounded terminal condition and a generator with quadratic growth in the $z$…
In this paper, our primary focus lies in the thorough investigation of a specific category of nonlinear fully coupled forward-backward stochastic differential equations involving time delays and advancements with the incorporation of…
We consider continuous-time stochastic optimal control problems featuring Conditional Value-at-Risk (CVaR) in the objective. The major difficulty in these problems arises from time-inconsistency, which prevents us from directly using…
In this work, we present a novel forward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs). Motivated by the fact that differential deep learning can…
We develop a deep learning model to effectively solve high-dimensional nonlinear parabolic partial differential equations (PDE). We follow Feynman-Kac formula to reformulate PDE into the equivalent stochastic control problem governed by a…
In the present work we employ, for the first time, backward stochastic differential equations (BSDEs) to study the optimal control of semi-Markov processes on finite horizon, with general state and action spaces. More precisely, we prove…
This paper develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve…
In this paper we are concerned with a new type of backward equations with anticipation which we call neutral backward stochastic functional differential equations. We obtain the existence and uniqueness and prove a comparison theorem. As an…
This paper addresses the inverse optimal control problem of finding the state weighting function that leads to a quadratic value function when the cost on the input is fixed to be quadratic. The paper focuses on a class of infinite horizon…
This project investigates numerical methods for solving fully coupled forward-backward stochastic differential equations (FBSDEs) of McKean-Vlasov type. Having numerical solvers for such mean field FBSDEs is of interest because of the…
We propose new numerical schemes for decoupled forward-backward stochastic differential equations (FBSDEs) with jumps, where the stochastic dynamics are driven by a $d$-dimensional Brownian motion and an independent compensated Poisson…