Dynamic Inventory Management with Mean-Field Competition
Abstract
In this presentation, Donnelly introduces a model where agents strive to maximize profits by selling perishable products, facing competitive influences from both their own quoted prices and those of other market agents. The proposed model is distinctly designed to capture this competitive effect, and Donnelly performs a comprehensive analysis in the mean-field limit, especially relevant as the number of agents becomes substantial. The mean-field Nash equilibrium is classified based on solutions to a Hamilton-Jacobi-Bellman equation and a consistency condition, paving the way for an innovative iterative numerical algorithm to compute equilibrium. The exploration delves into the properties of equilibrium pricing strategies and the broader dynamics of the market, shedding light on their dependency on competitive interaction strength and the capacity to oversell the product.
Watch recording ↗About the speaker
Ryan joined the Department of Mathematics in 2019 as a Lecturer of Financial Mathematics. In the past Ryan has been a Postdoctoral Researcher in the Swiss Finance Institute at Ecole polytechnique fédérale de Lausanne and a Research Associate in the Department of Applied Mathematics at the University of Washington. Ryan completed his PhD in Mathematics at the University of Toronto.