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The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range…

Other Condensed Matter · Physics 2008-12-02 Sergei Fedotov , Abby Tan

We study long-run market stability for repeated price competitions between two firms, where consumer demand depends on firms' posted prices and consumers' price expectations called reference prices. Consumers' reference prices vary over…

Computer Science and Game Theory · Computer Science 2022-03-23 Negin Golrezaei , Patrick Jaillet , Jason Cheuk Nam Liang

We investigate present some new statistical properties of order books. We analyse data from the Nasdaq and investigate (a) the statistics of incoming limit order prices, (b) the shape of the average order book, and (c) the typical life time…

Condensed Matter · Physics 2009-11-07 Marc Potters , Jean-Philippe Bouchaud

This paper investigates a multi-product stochastic inventory problem in which a cash-constrained online retailer can adopt order-based loan provided by some Chinese e-commerce platforms to speed up its cash recovery for deferred revenue. We…

Optimization and Control · Mathematics 2020-12-10 Zhen Chen , Ren-qian Zhang

Memory effects are ubiquitous in nature and are particularly relevant at the nanoscale where the dynamical properties of electrons and ions strongly depend on the history of the system, at least within certain time scales. We review here…

Mesoscale and Nanoscale Physics · Physics 2011-03-02 Yuriy V. Pershin , Massimiliano Di Ventra

The influence of class orderings in the evaluation of incremental learning has received very little attention. In this paper, we investigate the impact of class orderings for incrementally learned classifiers. We propose a method to compute…

Computer Vision and Pattern Recognition · Computer Science 2020-07-08 Marc Masana , Bartłomiej Twardowski , Joost van de Weijer

Many physical, biological, and engineered systems exhibit memory effects that challenge Markovian models. Fractional calculus provides nonlocal operators to capture hereditary dynamics. This survey connects modeling, analysis, and…

Optimization and Control · Mathematics 2025-12-16 Navid Mojahed , Hooman Fatoorehchi , Shima Nazari

We develop an empirical behavioural order-driven (EBOD) model, which consists of an order placement process and an order cancellation process. Price limit rules are introduced in the definition of relative price. The order placement process…

Computational Finance · Quantitative Finance 2022-08-23 Gao-Feng Gu , Xiong Xiong , Hai-Chuan Xu , Wei Zhang , Yong-Jie Zhang , Wei Chen , Wei-Xing Zhou

This paper analyzes stability conditions for wholesale electricity markets under real-time retail pricing and realistic consumption models with memory, which explicitly take into account previous electricity prices and consumption levels.…

Systems and Control · Computer Science 2017-02-21 Datong P. Zhou , Mardavij Roozbehani , Munther A. Dahleh , Claire J. Tomlin

This study addresses the difficulties associated with inventory management of products with stochastic demand. The objective is to find the optimal combination of order quantity and reorder point that maximizes profit while considering…

Computational Engineering, Finance, and Science · Computer Science 2023-10-05 Sarit Maitra , Vivek Mishra , Sukanya Kundu

In a discrete-time financial market model with instantaneous price impact, we find an asymptotically optimal strategy for an investor maximizing her expected wealth. The asset price is assumed to follow a process with negative memory. We…

Probability · Mathematics 2021-04-27 Miklós Rásonyi , Lóránt Nagy

Firms that price perishable resources -- airline seats, hotel rooms, seasonal inventory -- now routinely use demand predictions, but these predictions vary widely in quality. Under hard capacity constraints, acting on an inaccurate…

Optimization and Control · Mathematics 2026-03-27 Ruicheng Ao , Jiashuo Jiang , David Simchi-Levi

We consider the problem of learning from revealed preferences in an online setting. In our framework, each period a consumer buys an optimal bundle of goods from a merchant according to her (linear) utility function and current prices,…

Data Structures and Algorithms · Computer Science 2014-12-02 Kareem Amin , Rachel Cummings , Lili Dworkin , Michael Kearns , Aaron Roth

State of the art deep reinforcement learning algorithms are sample inefficient due to the large number of episodes they require to achieve asymptotic performance. Episodic Reinforcement Learning (ERL) algorithms, inspired by the mammalian…

Machine Learning · Computer Science 2024-06-07 Ismael T. Freire , Adrián F. Amil , Paul F. M. J. Verschure

In modern e-commerce and service operations, firms must jointly manage inventory replenishment and real-time order fulfillment to maximize profit under demand uncertainty. While each component has been studied extensively in isolation,…

Optimization and Control · Mathematics 2026-03-05 Zi Ling , Jiashuo Jiang , Linwei Xin

We study an online market-making problem in which a learner sequentially posts bid and ask prices for a single asset while interacting with traders holding private valuations. Unlike existing online learning formulations that assume fully…

Machine Learning · Computer Science 2026-05-20 Davide Maran , Marcello Restelli

An important question in economics is how people choose between different payments in the future. The classical normative model predicts that a decision maker discounts a later payment relative to an earlier one by an exponential function…

Theoretical Economics · Economics 2020-01-09 Alexander T. I. Adamou , Yonatan Berman , Diomides P. Mavroyiannis , Ole B. Peters

Episodic memory lets reinforcement learning algorithms remember and exploit promising experience from the past to improve agent performance. Previous works on memory mechanisms show benefits of using episodic-based data structures for…

Machine Learning · Computer Science 2021-06-17 Igor Kuznetsov , Andrey Filchenkov

The Solow-Swan equation is a cornerstone in the development of modern economic growth theory and continues to attract significant scholarly attention. This study incorporates memory effects into the classical Solow-Swan model by introducing…

General Finance · Quantitative Finance 2025-09-01 M. O. Aibinu , K. J. Duffy , S. Moyo

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…

Numerical Analysis · Mathematics 2016-12-22 John P. Hollkamp , Mihir Sen , Fabio Semperlotti
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