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Even in the face of deteriorating and highly volatile demand, firms often invest in, rather than discard, aging technologies. In order to study this phenomenon, we model the firm's profit stream as a Brownian motion with negative drift. At…

Optimization and Control · Mathematics 2019-01-08 H. Dharma Kwon

We consider a general class of dynamic resource allocation problems within a stochastic optimal control framework. This class of problems arises in a wide variety of applications, each of which intrinsically involves resources of different…

Optimization and Control · Mathematics 2018-01-08 Xuefeng Gao , Yingdong Lu , Mayank Sharma , Mark S. Squillante , Joost W. Bosman

We consider the problem of evaluating the quality of startup companies. This can be quite challenging due to the rarity of successful startup companies and the complexity of factors which impact such success. In this work we collect data on…

Applications · Statistics 2018-07-10 David Scott Hunter , Ajay Saini , Tauhid Zaman

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…

Optimization and Control · Mathematics 2014-01-21 Jim Dai , Dacheng Yao

In this paper, we consider an infinite horizon, continuous-review, stochastic inventory system in which cumulative customers' demand is price-dependent and is modeled as a Brownian motion. Excess demand is backlogged. The revenue is earned…

Optimization and Control · Mathematics 2018-07-12 Dacheng Yao

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…

Optimization and Control · Mathematics 2014-01-21 Jim Dai , Dacheng Yao

A continuous-time consumption-investment model with constraint is considered for a small investor whose decisions are the consumption rate and the allocation of wealth to a risk-free and a risky asset with logarithmic Brownian motion…

Portfolio Management · Quantitative Finance 2022-01-06 Zuo Quan Xu , Fahuai Yi

We introduce a simple framework in which market participants update their prior about an efficient price with a model-based learning process. We show that exponential intensities for the arrival of aggressive orders arise naturally in this…

Trading and Market Microstructure · Quantitative Finance 2021-09-29 Joffrey Derchu

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…

Optimization and Control · Mathematics 2022-11-28 Salvatore Federico , Giorgio Ferrari , Neofytos Rodosthenous

We present a Markovian market model driven by a hidden Brownian efficient price. In particular, we extend the queue-reactive model, making its dynamics dependent on the efficient price. Our study focuses on two sub-models: a signal-driven…

Trading and Market Microstructure · Quantitative Finance 2025-06-16 Emmanouil Sfendourakis

We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the price…

Pricing of Securities · Quantitative Finance 2011-11-14 Damir Filipović , Lane P. Hughston , Andrea Macrina

The Black-Litterman model is a framework for incorporating forward-looking expert views in a portfolio optimization problem. Existing work focuses almost exclusively on single-period problems with the forecast horizon matching that of the…

Portfolio Management · Quantitative Finance 2025-04-17 Anas Abdelhakmi , Andrew Lim

This paper studies how uncertainty about problem difficulty shapes problem-solving strategies. I develop a dynamic model where an agent solves a problem by brainstorming approaches of unknown quality and allocating a fixed effort budget…

Theoretical Economics · Economics 2026-04-02 Nicholas Wu

Online review communities are dynamic as users join and leave, adopt new vocabulary, and adapt to evolving trends. Recent work has shown that recommender systems benefit from explicit consideration of user experience. However, prior work…

Artificial Intelligence · Computer Science 2017-08-10 Subhabrata Mukherjee , Stephan Guennemann , Gerhard Weikum

We consider a continuous-review inventory system in which the setup cost of each order is a general function of the order quantity and the demand process is modeled as a Brownian motion with a positive drift. Assuming the holding and…

Optimization and Control · Mathematics 2020-09-03 Shuangchi He , Dacheng Yao , Hanqin Zhang

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…

Probability · Mathematics 2024-08-30 Adam Jonsson

We consider an investor who is dynamically informed about the future evolution of one of the independent Brownian motions driving a stock's price fluctuations. With linear temporary price impact the resulting optimal investment problem with…

Mathematical Finance · Quantitative Finance 2023-12-13 Peter Bank , Yan Dolinsky

We consider the problem of designing an expected-revenue maximizing mechanism for allocating multiple non-perishable goods of $k$ varieties to flexible consumers over $T$ time steps. In our model, a random number of goods of each variety…

Computer Science and Game Theory · Computer Science 2020-07-08 Shiva Navabi , Ashutosh Nayyar

Consider a storage system where the content is driven by a Brownian motion absent control. At any time, one may increase or decrease the content at a cost proportional to the amount of adjustment. A decrease of the content takes effect…

Probability · Mathematics 2016-08-05 Zhen Xu , Jiheng Zhang , Rachel Q. Zhang

When launching new products, firms face uncertainty about market reception. Online reviews provide valuable information not only to consumers but also to firms, allowing firms to adjust the product characteristics, including its selling…

Machine Learning · Computer Science 2024-04-24 José Correa , Mathieu Mari , Andrew Xia
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