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The Economics of Continuous-Time Finance (Hardcover)
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The Economics of Continuous-Time Finance (Hardcover)
Series: The MIT Press
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An introduction to economic applications of the theory of
continuous-time finance that strikes a balance between mathematical
rigor and economic interpretation of financial market regularities.
This book introduces the economic applications of the theory of
continuous-time finance, with the goal of enabling the construction
of realistic models, particularly those involving incomplete
markets. Indeed, most recent applications of continuous-time
finance aim to capture the imperfections and dysfunctions of
financial markets-characteristics that became especially apparent
during the market turmoil that started in 2008. The book begins by
using discrete time to illustrate the basic mechanisms and
introduce such notions as completeness, redundant pricing, and no
arbitrage. It develops the continuous-time analog of those
mechanisms and introduces the powerful tools of stochastic
calculus. Going beyond other textbooks, the book then focuses on
the study of markets in which some form of incompleteness,
volatility, heterogeneity, friction, or behavioral subtlety arises.
After presenting solutions methods for control problems and related
partial differential equations, the text examines portfolio
optimization and equilibrium in incomplete markets, interest rate
and fixed-income modeling, and stochastic volatility. Finally, it
presents models where investors form different beliefs or suffer
frictions, form habits, or have recursive utilities, studying the
effects not only on optimal portfolio choices but also on
equilibrium, or the price of primitive securities. The book strikes
a balance between mathematical rigor and the need for economic
interpretation of financial market regularities, although with an
emphasis on the latter.
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