相关论文: A segment-wise dynamic programming algorithm for B…
This work deals with the numerical approximation of backward stochastic differential equations (BSDEs). We propose a new algorithm which is based on the regression-later approach and the least squares Monte Carlo method. We give some…
In this paper, we design a novel algorithm based on Least-Squares Monte Carlo (LSMC) in order to approximate the solution of discrete time Backward Stochastic Differential Equations (BSDEs). Our algorithm allows massive parallelization of…
Recently proposed numerical algorithms for solving high-dimensional nonlinear partial differential equations (PDEs) based on neural networks have shown their remarkable performance. We review some of them and study their convergence…
We propose a new multistep deep learning-based algorithm for the resolution of moderate to high dimensional nonlinear backward stochastic differential equations (BSDEs) and their corresponding parabolic partial differential equations (PDE).…
The goal of this work is to parallelize the multistep scheme for the numerical approximation of the backward stochastic differential equations (BSDEs) in order to achieve both, a high accuracy and a reduction of the computation time as…
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…
In this article we design a novel quasi-regression Monte Carlo algorithm in order to approximate the solution of discrete time backward stochastic differential equations (BSDEs), and we analyze the convergence of the proposed method. The…
We propose an accurate data-driven numerical scheme to solve Stochastic Differential Equations (SDEs), by taking large time steps. The SDE discretization is built up by means of a polynomial chaos expansion method, on the basis of…
This paper proposes a polynomial-time algorithm to construct the monotone stepwise curve that minimizes the sum of squared errors with respect to a given cloud of data points. The fitted curve is also constrained on the maximum number of…
In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are…
Safe and economic operation of networked systems is often challenging. Optimization-based schemes are frequently considered, since they achieve near-optimality while ensuring safety via the explicit consideration of constraints. In…
We introduce new variants of classical regression-based algorithms for optimal stopping problems based on computation of regression coefficients by Monte Carlo approximation of the corresponding $L^2$ inner products instead of the…
Novel multi-step predictor-corrector numerical schemes have been derived for approximating decoupled forward-backward stochastic differential equations (FBSDEs). The stability and high order rate of convergence of the schemes are rigorously…
We develop a multilevel approach to compute approximate solutions to backward differential equations (BSDEs). The fully implementable algorithm of our multilevel scheme constructs sequential martingale control variates along a sequence of…
We introduce a novel dynamic learning-rate scheduling scheme grounded in theory with the goal of simplifying the manual and time-consuming tuning of schedules in practice. Our approach is based on estimating the locally-optimal stepsize,…
We propose a probabilistic numerical algorithm to solve Backward Stochastic Differential Equations (BSDEs) with nonnegative jumps, a class of BSDEs introduced in [9] for representing fully nonlinear HJB equations. In particular, this allows…
We design a numerical scheme for solving a Dynamic Programming equation with Malliavin weights arising from the time-discretization of backward stochastic differential equations with the integration by parts-representation of the…
An overview of advanced dynamical algorithms capable of spanning the widely disparate time scales that govern the decay of metastable phases in discrete spin models is presented. The algorithms discussed include constrained transfer-matrix,…
We study the fixed design segmented regression problem: Given noisy samples from a piecewise linear function $f$, we want to recover $f$ up to a desired accuracy in mean-squared error. Previous rigorous approaches for this problem rely on…
Nonlinear differential equations (DEs) are used in a wide range of scientific problems to model complex dynamic systems. The differential equations often contain unknown parameters that are of scientific interest, which have to be estimated…