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Time-Inconsistent Control Theory with Finance Applications (Hardcover, 1st ed. 2021)
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Time-Inconsistent Control Theory with Finance Applications (Hardcover, 1st ed. 2021)
Series: Springer Finance
Expected to ship within 10 - 15 working days
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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.
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