Time-Inconsistent Control Theory with Finance Applications

This book is devoted to problems of stochastic control and stopping that are time inconsistent in the sense that they do not admit a Bellman optimality principle. These problems are cast in a game-theoretic framework, with the focus on subgame-perfect Nash equilibrium strategies. The general theory is illustrated with a number of finance applications.

In dynamic choice problems, time inconsistency is the rule rather than the exception. Indeed, as Robert H. Strotz pointed out in his seminal 1955 paper, relaxing the widely used ad hoc assumption of exponential discounting gives rise to time inconsistency. Other famous examples of time inconsistency include mean-variance portfolio choice and prospect theory in a dynamic context. For such models, the very concept of optimality becomes problematic, as the decision maker’s preferences change over time in a temporally inconsistent way. In this book, a time-inconsistent problem is viewed as a non-cooperative game between the agent’s current and future selves, with the objective of finding intrapersonal equilibria in the game-theoretic sense. A range of finance applications are provided, including problems with non-exponential discounting, mean-variance objective, time-inconsistent linear quadratic regulator, probability distortion, and market equilibrium with time-inconsistent preferences.

Time-Inconsistent Control Theory with Finance Applications offers the first comprehensive treatment of time-inconsistent control and stopping problems, in both continuous and discrete time, and in the context of finance applications. Intended for researchers and graduate students in the fields of finance and economics, it includes a review of the standard time-consistent results, bibliographical notes, as well as detailed examples showcasing time inconsistency problems. For the reader unacquainted with standard arbitrage theory, an appendix provides a toolbox of material needed for the book.

本書專注於時間不一致的隨機控制和停止問題，這些問題不符合貝爾曼最優性原則。這些問題以博弈論框架來討論，重點在於子博弈完美納什均衡策略。通過多個金融應用案例來說明一般理論。

在動態選擇問題中，時間不一致是常見的情況。事實上，正如羅伯特·H·斯特羅茨在他1955年的開創性論文中指出的那樣，放寬廣泛使用的指數貼現的臨時假設會導致時間不一致。其他著名的時間不一致例子包括均值-方差投資組合選擇和動態情景理論。對於這樣的模型，最優性的概念變得有問題，因為決策者的偏好隨時間以不一致的方式變化。在本書中，時間不一致的問題被視為代理人當前和未來自我的非合作博弈，目標是在博弈論意義上找到個人內部均衡。書中提供了一系列金融應用案例，包括非指數貼現、均值-方差目標、時間不一致的線性二次調節器、概率扭曲和時間不一致偏好下的市場均衡。

《具有金融應用的時間不一致控制理論》是第一本全面介紹連續和離散時間下時間不一致控制和停止問題的書籍，並且涉及金融應用。適用於金融和經濟領域的研究人員和研究生，書中包括對標準時間一致結果的回顧、參考文獻注釋以及詳細的時間不一致問題示例。對於不熟悉標準套利理論的讀者，附錄提供了本書所需的工具材料。