Related papers: Relative entropy-regularized robust optimal order …
We characterize the value of swing contracts in continuous time as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation with suitable boundary conditions. The case of contracts with penalties is straightforward, and in that…
Scenario reduction algorithms can be an effective means to provide a tractable description of the uncertainty in optimal control problems. However, they might significantly compromise the performance of the controlled system. In this paper,…
We give a new formulation of the relative arbitrage problem from stochastic portfolio theory that asks for a time horizon beyond which arbitrage relative to the market exists in all ``sufficiently volatile'' markets. In our formulation,…
In financial markets, the order flow, defined as the process assuming value one for buy market orders and minus one for sell market orders, displays a very slowly decaying autocorrelation function. Since orders impact prices, reconciling…
The Koopman operator enables simplified representations for nonlinear systems in data-driven optimal control, but the accompanying uncertainties inevitably induce deviations in the optimal controller and associated value function. This…
We propose a stochastic first-order algorithm to learn the rationality parameters of simultaneous and non-cooperative potential games, i.e., the parameters of the agents' optimization problems. Our technique combines (i.) an active-set step…
We study a class of deterministic mean field games and related optimal control problems, with a finite time horizon and in which the state space is a network. An agent controls her velocity, and, when she occupies a vertex, she can either…
In this paper, we consider the classic stochastic (dynamic) knapsack problem, a fundamental mathematical model in revenue management, with general time-varying random demand. Our main goal is to study the optimal policies, which can be…
The uncertainties in plant dynamics remain a challenge for nonlinear control problems. This paper develops a ternary policy iteration (TPI) algorithm for solving nonlinear robust control problems with bounded uncertainties. The controller…
Information processing abilities of active matter are studied in the reservoir computing (RC) paradigm to infer the future state of a chaotic signal. We uncover an exceptional regime of agent dynamics that has been overlooked previously. It…
We study a generic principal-agent problem in continuous time on a finite time horizon. We introduce a framework in which the agent is allowed to employ measure-valued controls and characterise the continuation utility as a solution to a…
In this paper, we study the problem of multiple stochastic agents interacting in a dynamic game scenario with continuous state and action spaces. We define a new notion of stochastic Nash equilibrium for boundedly rational agents, which we…
This article proposes an improved trajectory optimization approach for stochastic optimal control of dynamical systems affected by measurement noise by combining optimal control with maximum likelihood techniques to improve the reduction of…
In this paper we propose a new way of proving the value of a firm that is currently producing a certain product and faces the option to exit the market. The problem of optimal exiting is an optimal stopping problem, that can be solved using…
This paper introduces a new algorithmic execution model that integrates interbank limit and market orders with internal liquidity generated through market making. Based on the Cartea et al.\cite{cartea2015algorithmic} framework, we…
This paper studies the continuous-time reinforcement learning (RL) for optimal switching problems across multiple regimes. We consider a type of exploratory formulation under entropy regularization where the agent randomizes both the timing…
Despite the many recent advances in reinforcement learning (RL), the question of learning policies that robustly satisfy state constraints under unknown disturbances remains open. In this paper, we offer a new perspective on achieving…
A general time-inconsistent optimal control problem is considered for stochastic differential equations with deterministic coefficients. Under suitable conditions, a Hamilton-Jacobi-Bellman type equation is derived for the equilibrium value…
This paper proposes an off-policy risk-sensitive reinforcement learning based control framework for stabilization of a continuous-time nonlinear system that subjects to additive disturbances, input saturation, and state constraints. By…
In this paper, we first establish the dynamic programming principle for stochastic optimal control problems defined on compact Riemannian manifolds without boundary. Subsequently, we derive the associated Hamilton-Jacobi-Bellman (HJB)…