Related papers: Dynamic pricing in retail with diffusion process d…
We formulate a continuous-time competitive equilibrium model of irreversible capacity investment in which a continuum of heterogeneous producers supplies a single non-durable good subject to exogenous stochastic demand. Each producer…
We consider a profit maximization problem in an urban mobility on-demand service, of which the operator owns a fleet, provides both exclusive and shared trip services, and dynamically determines prices of offers. With knowledge of the…
For continuous systems modeled by dynamical equations such as ODEs and SDEs, Bellman's Principle of Optimality takes the form of the Hamilton-Jacobi-Bellman (HJB) equation, which provides the theoretical target of reinforcement learning…
Minimizing the peak power consumption and matching demand to supply, under fixed threshold polices, are two key requirements for the success of the future electricity market. In this work, we consider dynamic pricing methods to minimize the…
In this paper infinite horizon optimal control problems for nonlinear high-dimensional dynamical systems are studied. Nonlinear feedback laws can be computed via the value function characterized as the unique viscosity solution to the…
A system manager makes dynamic pricing and dispatch control decisions in a queueing network model motivated by ride-hailing applications. A novel feature of the model is that it incorporates travel times. Unfortunately, this renders the…
A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and…
In this paper we study the single-item revenue management problem, with no information given about the demand trajectory over time. When the item is sold through accepting/rejecting different fare classes, Ball and Queyranne (2009) have…
Time or money? That is a question! In this paper, we consider this dilemma in the pricing regime, in which we try to find the optimal pricing scheme for identical items with heterogenous time-sensitive buyers. We characterize the…
This paper introduces a jump-diffusion pricing model specifically designed for algorithmic trading and high-frequency trading (HFT). The model incorporates independent jump and diffusion processes, providing a more precise representation of…
Conventional harvesting problems for natural resources often assume physiological homogeneity of the body length/weight among individuals. However, such assumptions generally are not valid in real-world problems, where heterogeneity plays…
In this research, we develop a trading strategy for the discrete-time optimal liquidation problem of large order trading with different market microstructures in an illiquid market. In this framework, the flow of orders can be viewed as a…
The paper studies a system of Hamilton-Jacobi equations, arising from a stochastic optimal debt management problem in an infinite time horizon with exponential discount, modeled as a noncooperative interaction between a borrower and a pool…
We consider fully nonlinear Hamilton-Jacobi-Bellman equations associated to diffusion control problems involving a finite set-valued (or switching) control and possibly a continuum-valued control. In previous works (Akian, Fodjo, 2016 and…
We explore the approximation of feedback control of integro-differential equations containing a fractional Laplacian term. To obtain feedback control for the state variable of this nonlocal equation we use the Hamilton--Jacobi--Bellman…
A classical problem in ergodic continuous time control consists of studying the limit behavior of the optimal value of a discounted cost functional with infinite horizon as the discount factor $\lambda$ tends to zero. In the literature,…
This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. After studying continuity properties of the…
We study the problem of dynamically trading multiple futures contracts with different underlying assets. To capture the joint dynamics of stochastic bases for all traded futures, we propose a new model involving a multi-dimensional scaled…
We study policy iteration (PI) for deterministic infinite-horizon discounted optimal control problems, whose value function is characterized by a stationary Hamilton--Jacobi--Bellman (HJB) equation. At the PDE level, PI is fundamentally…
We consider a discounted reward control problem in continuous time stochastic environment where the discount rate might be an unbounded function of the control process. We provide a set of general assumptions to ensure that there exists a…