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Optimal execution is an important problem faced by any trader. Most solutions are based on the assumption of constant market impact, while liquidity is known to be dynamic. Moreover, models with time-varying liquidity typically assume that…
We study optimal contract design for large populations of heterogeneous agents whose actions generate network spillovers represented by an interaction function. In a linear-quadratic framework, we solve the finite-agent problem and its…
This paper introduces a reinforcement learning-based tracking control approach for a class of nonlinear systems using neural networks. In this approach, adversarial attacks were considered both in the actuator and on the outputs. This…
We propose a new numerical method for solving the Hamilton-Jacobi-Bellman quasi-variational inequality associated with the combined impulse and stochastic optimal control problem over a finite time horizon. Our method corresponds to an…
While sequential task assignment for a single agent has been widely studied, such problems in a multi-agent setting, where the agents have heterogeneous task preferences or capabilities, remain less well-characterized. We study a…
This paper tackles a multi-agent bandit setting where $M$ agents cooperate together to solve the same instance of a $K$-armed stochastic bandit problem. The agents are \textit{heterogeneous}: each agent has limited access to a local subset…
In this paper, we focus on the problem of optimal portfolio-consumption policies in a multi-asset financial market, where the n risky assets follow Exponential Ornstein-Uhlenbeck processes, along with one risk-free bond. The investor's…
In this paper, we first conduct a study of the portfolio selection problem, incorporating both exogenous (proportional) and endogenous (resulting from liquidity risk, characterized by a stochastic process) transaction costs through the…
We study an agency problem between a leader (the principal) seeking to design an optimal incentive scheme to a follower (the agent) to increase the value of a risky project subjected to accidents and volatility uncertainty. The agency…
We study the problem of utility maximization from terminal wealth in which an agent optimally builds her portfolio by investing in a bond and a risky asset. The asset price dynamics follow a diffusion process with regime-switching…
This paper presents the optimal control and synchronization problem of a multilevel network of R\"ossler chaotic oscillators. Using the Hamilton-Jacobi-Bellman (HJB) technique, the optimal control law with three-state variables feedback is…
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…
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…
When randomness in demand affects the sales of a product, retailers use dynamic pricing strategies to maximize their profits. In this article, we formulate the pricing problem as a continuous-time stochastic optimal control problem and find…
This paper studies an optimal consensus problem for a group of heterogeneous high-order agents with unknown control directions. Compared with existing consensus results, the consensus point is further required to an optimal solution to some…
The ad-trading desks of media-buying agencies are increasingly relying on complex algorithms for purchasing advertising inventory. In particular, Real-Time Bidding (RTB) algorithms respond to many auctions -- usually Vickrey auctions --…
In this paper, a distributed optimal steady-state regulation problem is formulated and investigated for heterogeneous linear multi-agent systems subject to external disturbances. We aim to steer this high-order multi-agent network to a…
We mathematically analyze and numerically study an actor-critic machine learning algorithm for solving high-dimensional Hamilton-Jacobi-Bellman (HJB) partial differential equations from stochastic control theory. The architecture of the…
Mixed optimal stopping and stochastic control problems define variational inequalities with non-linear Hamilton-Jacobi-Bellman (HJB) operators, whose numerical solution is notoriously difficult and lack of reliable benchmarks. We first use…
This paper investigates the distributed optimal output consensus problem of heterogeneous linear multi-agent systems over weight-unbalanced directed networks. A novel distributed continuous-time state feedback controller is proposed to…