Stochastic Linear Quadratic Optimal Control Theory Differential Games And Mean Field Problems
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Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems
This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents results for two-player differential games and mean-field optimal control problems in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, the book identifies, for the first time, the interconnections between the existence of open-loop and closed-loop Nash equilibria, solvability of the optimality system, and solvability of the associated Riccati equation, and also explores the open-loop solvability of mean-filed linear-quadratic optimal control problems. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.
Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions
This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents the results in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, it precisely identifies, for the first time, the interconnections between three well-known, relevant issues – the existence of optimal controls, solvability of the optimality system, and solvability of the associated Riccati equation. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.
The Unaffordable Price of Static Decision-making Models
Author: Fouad El Ouardighi
language: en
Publisher: Springer Nature
Release Date: 2025-07-01
At the 15th Viennese Workshop on Optimal Control and Dynamic Games, held in July 2022, experts in economics and the management sciences identified a concerning trend: static decision-making models, while less effective than dynamic ones, are becoming increasingly prevalent. This book aims to address the economic and social costs associated with reliance on static models and to demonstrate the advantages of applying dynamic approaches. Static models may be easier to formulate, but they often overlook the long-term consequences of decisions, promoting myopic practices that can lead to poor outcomes. In contrast, dynamic models foster a more comprehensive perspective, enabling foresight in decision-making – which is crucial for issues involving stock variables, such as pollution, reputation, and inventory. The book explores the limitations of static models, including their inability to capture long-term outcomes, history-dependent solutions, and the impact of abrupt contextual changes. It also highlights recent advances in dynamic modeling techniques that can enhance accuracy and help adapt to complex decision-making environments. By promoting the shift from static to dynamic models, this book aspires to open new research opportunities and provide valuable insights for researchers, students, policymakers, and managers in the fields of economics and the management sciences.