Related papers: A deep learning-driven iterative scheme for high-d…
The paper studies a system of first order Hamilton-Jacobi equations with discontinuous coefficients, arising from a model of deterministic optimal debt management in infinite time horizon, with exponential discount and currency devaluation.…
An optimal control problem is considered for a stochastic differential equation containing a state-dependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is…
Option contracts on two underlying assets within uncertain volatility models have their worst-case and best-case prices determined by a two-dimensional (2D) Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE) with…
With the continuous advancement in autonomous systems, it becomes crucial to provide robust safety guarantees for safety-critical systems. Hamilton-Jacobi Reachability Analysis is a formal verification method that guarantees performance and…
This paper proposes a Deep Reinforcement Learning algorithm for financial portfolio trading based on Deep Q-learning. The algorithm is capable of trading high-dimensional portfolios from cross-sectional datasets of any size which may…
The Hamilton-Jacobi-Bellman equation arising from the optimal portfolio selection problem is studied by means of the maximal monotone operator method. The existence and uniqueness of a solution to the Cauchy problem for the nonlinear…
In this report we derive the strategic (deterministic) allocation to bonds and stocks resulting in the optimal mean-variance trade-off on a given investment horizon. The underlying capital market features a mean-reverting process for equity…
We propose a neural network approach for solving high-dimensional optimal control problems. In particular, we focus on multi-agent control problems with obstacle and collision avoidance. These problems immediately become high-dimensional,…
Solving the Hamilton-Jacobi-Bellman equation is important in many domains including control, robotics and economics. Especially for continuous control, solving this differential equation and its extension the Hamilton-Jacobi-Isaacs…
A new algorithm for time dependent Hamilton Jacobi equations on networks, based on semi Lagrangian scheme, is proposed. It is based on the definition of viscosity solution for this kind of problems recently given in. A thorough convergence…
Path Integral Control methods were developed for stochastic optimal control covering a wide class of finite horizon formulations with control affine nonlinear dynamics. Characteristic for this class is that the HJB equation is linear and…
Two key challenges in optimal control include efficiently solving high-dimensional problems and handling optimal control problems with state-dependent running costs. In this paper, we consider a class of optimal control problems whose…
We propose a novel data-driven neural network (NN) optimization framework for solving an optimal stochastic control problem under stochastic constraints. Customized activation functions for the output layers of the NN are applied, which…
This paper considers optimal control of dynamical systems which are represented by nonlinear stochastic differential equations. It is well-known that the optimal control policy for this problem can be obtained as a function of a value…
In a previous work (Akian, Fodjo, 2016), we introduced a lower complexity probabilistic max-plus numerical method for solving fully nonlinear Hamilton-Jacobi-Bellman equations associated to diffusion control problems involving a finite…
In this paper, we explore the use of a deep residual U-net with self-attention to solve the the continuous time time-consistent mean variance optimal trade execution problem for multiple agents and assets. Given a finite horizon we…
We propose a supervised learning scheme for the first order Hamilton--Jacobi PDEs in high dimensions. The scheme is designed by using the geometric structure of Wasserstein Hamiltonian flows via a density coupling strategy. It is…
The present paper provides a study of high-dimensional statistical arbitrage that combines factor models with the tools from stochastic control, obtaining closed-form optimal strategies which are both interpretable and computationally…
We study a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class includes some problems arising in economics, in particular the so-called models with time to…
We propose a machine learning algorithm for solving finite-horizon stochastic control problems based on a deep neural network representation of the optimal policy functions. The algorithm has three features: (1) It can solve…