Related papers: A deep primal-dual BSDE method for optimal stoppin…
High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in…
We study maximum likelihood estimation for spatial generalized linear mixed models with Gaussian process approximations using a stochastic Newton-Raphson algorithm. We consider two Gaussian Process approximations in this context: spectral…
In this paper we introduce and study the concept of optimal and surely optimal dual martingales in the context of dual valuation of Bermudan options, and outline the development of new algorithms in this context. We provide a…
Considering generating samples with high rewards, we focus on optimizing deep neural networks parameterized stochastic differential equations (SDEs), the advanced generative models with high expressiveness, with policy gradient, the leading…
We present a novel deep learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization…
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…
We introduce the Optimizing a Discrete Loss (ODIL) framework for the numerical solution of Partial Differential Equations (PDE) using machine learning tools. The framework formulates numerical methods as a minimization of discrete residuals…
In this paper, we first establish the reflected backward stochastic difference equations with finite state (FS-RBSDEs for short). Then we explore the Existence and Uniqueness Theorem as well as the Comparison Theorem by "one step" method.…
Optimization-based PDE solvers that minimize scalar loss functions have gained increasing attention in recent years. These methods either define the loss directly over discrete variables, as in Optimizing a Discrete Loss (ODIL), or…
A new deep-learning neural network architecture based on high-order weak approximation algorithms for stochastic differential equations (SDEs) is proposed. The architecture enables the efficient learning of martingales by deep learning…
Recent advances in deep learning makes solving parabolic partial differential equations (PDEs) in high dimensional spaces possible via forward-backward stochastic differential equation (FBSDE) formulations. The implementation of most…
This paper introduces a new formulation for stochastic optimal control and stochastic dynamic optimization that ensures safety with respect to state and control constraints. The proposed methodology brings together concepts such as…
We propose an approach to applying neural networks on linear parabolic variational inequalities. We use loss functions that directly incorporate the variational inequality on the whole domain to bypass the need to determine the stopping…
We develop a novel stochastic primal dual splitting method with Bregman distances for solving a structured composite problems involving infimal convolutions in non-Euclidean spaces. The sublinear convergence in expectation of the…
We study a backward stochastic differential equation whose terminal condition is an integrable function of a local martingale and generator has bounded growth in $z$. When the local martingale is a strict local martingale, the BSDE admits…
In this work, we revisit a classical incremental implementation of the primal-descent dual-ascent gradient method used for the solution of equality constrained optimization problems. We provide a short proof that establishes the linear…
There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the…
We propose a new approach to solve optimal stopping problems via simulation. Working within the backward dynamic programming/Snell envelope framework, we augment the methodology of Longstaff-Schwartz that focuses on approximating the…
We study utility maximization problem for general utility functions using dynamic programming approach. We consider an incomplete financial market model, where the dynamics of asset prices are described by an $R^d$-valued continuous…
We introduce a new type of reflected backward stochastic differential equations (BSDEs) for which the reflection constraint is imposed on its main solution component, denoted as $Y$ by convention, but in terms of its conditional expectation…