Related papers: Continuous Inventory Models of Diffusion Type: Lon…
We investigate propagation of convexity and convex ordering on a typical discrete-time stochastic optimal control problem, namely the pricing of swing option. The dynamics of the underlying asset is modelled by the Euler scheme of a…
We consider an inventory system in which inventory level fluctuates as a Brownian motion in the absence of control. The inventory continuously accumulates cost at a rate that is a general convex function of the inventory level, which can be…
This paper investigates a stochastic inventory management problem in which a cash-constrained small retailer periodically purchases a product from suppliers and sells it to a market while facing non-stationary demands. In each period, the…
We study a simple singular control problem for a Brownian motion with constant drift and variance reflected at the origin. Exerting control pushes the process towards the origin and generates a concave increasing state-dependent yield which…
We solve a version of the optimal trade execution problem when the mid asset price follows a displaced diffusion. Optimal strategies in the adapted class under various risk criteria, namely value-at-risk, expected shortfall and a new…
We consider the dynamic inventory problem with non-stationary demands. It has long been known that non-stationary (s, S) policies are optimal for this problem. However, finding optimal policy parameters remains a computational challenge as…
Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…
In this paper we study a continuous time stochastic inventory model for a commodity traded in the spot market and whose supply purchase is affected by price and demand uncertainty. A firm aims at meeting a random demand of the commodity at…
The paper studies approximations and control of a processor sharing (PS) server where the service rate depends on the number of jobs occupying the server. The control of such a system is implemented by imposing a limit on the number of jobs…
In this paper, we consider a rather general linear evolution equation of fractional type, namely a diffusion type problem in which the diffusion operator is the $s$th power of a positive definite operator having a discrete spectrum in…
This paper studies a {\it reversible} investment problem where a social planner aims to control its capacity production in order to fit optimally the random demand of a good. Our model allows for general diffusion dynamics on the demand as…
Transport of point-size Brownian particles under the influence of a constant and uniform force field through a three-dimensional channel with smoothly varying periodic cross-section is investigated. Here, we employ an asymptotic analysis in…
We consider the following two deterministic inventory optimization problems over a finite planning horizon $T$ with non-stationary demands. (a) Submodular Joint Replenishment Problem: This involves multiple item types and a single retailer…
A well-know control policy in stochastic inventory control is the (R, s, S) policy, in which inventory is raised to an order-up-to-level S at a review instant R whenever it falls below reorder-level s. To date, little or no work has been…
This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an…
We consider the scheduling control problem for a family of unitary networks under heavy traffic, with general interarrival and service times, probabilistic routing and infinite horizon discounted linear holding cost. A natural…
This paper studies convergence properties of optimal values and actions for discounted and average-cost Markov Decision Processes (MDPs) with weakly continuous transition probabilities and applies these properties to the stochastic…
Flow matching has emerged as a powerful framework for generative modeling, offering computational advantages over diffusion models by leveraging deterministic Ordinary Differential Equations (ODEs) instead of stochastic dynamics. While…
We study the problem of optimally managing an inventory with unknown demand trend. Our formulation leads to a stochastic control problem under partial observation, in which a Brownian motion with non-observable drift can be singularly…
We propose a variational formulation of an inverse problem in continuous-time stochastic control, aimed at identifying control costs consistent with a given distribution over trajectories. The formulation is based on minimizing the…