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Stochastic Finance - An Introduction in Discrete Time (Paperback, 4th rev. ed.)
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Stochastic Finance - An Introduction in Discrete Time (Paperback, 4th rev. ed.)
Series: De Gruyter Textbook
Expected to ship within 10 - 15 working days
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This book is an introduction to financial mathematics. It is
intended for graduate students in mathematics and for researchers
working in academia and industry. The focus on stochastic models in
discrete time has two immediate benefits. First, the probabilistic
machinery is simpler, and one can discuss right away some of the
key problems in the theory of pricing and hedging of financial
derivatives. Second, the paradigm of a complete financial market,
where all derivatives admit a perfect hedge, becomes the exception
rather than the rule. Thus, the need to confront the intrinsic
risks arising from market incomleteness appears at a very early
stage. The first part of the book contains a study of a simple
one-period model, which also serves as a building block for later
developments. Topics include the characterization of arbitrage-free
markets, preferences on asset profiles, an introduction to
equilibrium analysis, and monetary measures of financial risk. In
the second part, the idea of dynamic hedging of contingent claims
is developed in a multiperiod framework. Topics include martingale
measures, pricing formulas for derivatives, American options,
superhedging, and hedging strategies with minimal shortfall risk.
This fourth, newly revised edition contains more than one hundred
exercises. It also includes material on risk measures and the
related issue of model uncertainty, in particular a chapter on
dynamic risk measures and sections on robust utility maximization
and on efficient hedging with convex risk measures. Contents: Part
I: Mathematical finance in one period Arbitrage theory Preferences
Optimality and equilibrium Monetary measures of risk Part II:
Dynamic hedging Dynamic arbitrage theory American contingent claims
Superhedging Efficient hedging Hedging under constraints Minimizing
the hedging error Dynamic risk measures
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