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.
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The first part of the book studies a simple one-period model which 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 risk.
In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Such models are typically incomplete: They involve intrinsic risks which cannot be hedged away completely. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. In addition to many corrections and improvements, this second edition contains several new sections, including a systematic discussion of law-invariant risk measures and of the connections between American options, superhedging, and dynamic risk measures.
Open Access. About Us. English Deutsch. Sign In Create Profile. Advanced Search Help. Subject Areas Subject Areas. Series: De Gruyter Studies in Mathematics, Overview Contents This book is an introduction to financial mathematics.
Standard refence book for stochastic finance in discrete time Now with exercises Suitable for students, researchers and practioneers. Author Information. Details Edition: 2nd rev. Reprint Audience: Graduate students in mathematics, researchers working in academia and industry; academic libraries. Sign Up. Primary occupation. Subject area. Sign up for free. De Gruyter Mouton. De Gruyter Oldenbourg. De Gruyter Saur. Deutscher Kunstverlag. Edition Klaus Schwarz. Help Center. Our Locations.
ISBN 13: 9783110463446
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.
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