Related papers: A Weak Convergence Approach to Inventory Control U…
Demand forecasting plays an important role in many inventory control problems. To mitigate the potential harms of model misspecification, various forms of distributionally robust optimization have been applied. Although many of these…
In this work we present an extension of the technique of the order reduction to higher perturbative approximations in an iterative fashion. The intention is also to analyze more carefully the conditions for the validity of the order…
The article poses a general model for optimal control subject to information constraints, motivated in part by recent work of Sims and others on information-constrained decision-making by economic agents. In the average-cost optimal control…
We study optimal control of diffusions with slow and fast variables and address a question raised by practitioners: is it possible to first eliminate the fast variables before solving the optimal control problem and then use the optimal…
We study a time-inconsistent singular stochastic control problem for a general one-dimensional diffusion, where time-inconsistency arises from a non-exponential discount function. To address this, we adopt a game-theoretic framework and…
We consider a stochastic system whose uncontrolled state dynamics are modelled by a general one-dimensional It\^{o} diffusion. The control effort that can be applied to this system takes the form that is associated with the so-called…
We study the optimal control of storage which is used for arbitrage, i.e. for buying a commodity when it is cheap and selling it when it is expensive. Our particular concern is with the management of energy systems, although the results are…
In this paper, we present a simple microeconomic model with linear continuous-time dynamics that describes a production-inventory system with debt repayment. This model is formulated in terms of optimal control and its exact solutions are…
Over the recent past data-driven algorithms for solving stochastic optimal control problems in face of model uncertainty have become an increasingly active area of research. However, for singular controls and underlying diffusion dynamics…
We consider the problem of maximizing the expected average reward obtained over an infinite time horizon by $n$ weakly coupled Markov decision processes. Our setup is a substantial generalization of the multi-armed restless bandit problem…
Drift diffusion models (DDMs) have found widespread use in computational neuroscience and other fields. They model evidence accumulation in simple decision tasks as a stochastic process drifting towards a decision barrier. In models where…
Newsvendor problem is an extensively researched topic in inventory management. In this class of inventory problems, shortage and excess costs are considered to be proportional to the quantity lost. But, for critical goods or commodities,…
The main goal of this paper is to derive sufficient conditions for the existence of an optimal control strategy for the long run average continuous control problem of piecewise deterministic Markov processes (PDMP's) taking values in a…
Diffusion models have become prevalent in generative modeling due to their ability to sample from complex distributions. To improve the quality of generated samples and their compliance with user requirements, two commonly used methods are:…
We map the problem of diffusion in the quenched trap model onto a new stochastic process: Brownian motion which is terminated at the coverage "time" ${\cal S}_\alpha=\sum_{x=-\infty} ^\infty (n_x)^\alpha$ with $n_x$ being the number of…
In this article, we present a general methodology for stochastic control problems driven by the Brownian motion filtration including non-Markovian and non-semimartingale state processes controlled by mutually singular measures. The main…
The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…
We study the canonical periodic review lost sales inventory system with positive leadtime and independent and identically distributed (i.i.d.) demand under the average cost criterion. We demonstrate that the relative value function under…
Diffusion models have recently emerged as effective generative frameworks for trajectory optimization, capable of producing high-quality and diverse solutions. However, training these models in a purely data-driven manner without explicit…
High-tech systems are typically produced in two stages: 1) Production of components using specialized equipment and staff; 2) System assembly/integration. Component production capacity is subject to fluctuations, causing a high risk of…