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This book is an introduction to financial mathematics.
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.
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.
"This book provides a fairly complete treatment of the most important probabilistic aspects of financial mathematics (or stochastic finance). [...] It is a worthwhile addition to the literature and will serve as highly recommended reading for students in the subject area for some years to come." Mathematical Reviews (review of the first edition)
"Since the appearance of the first edition in 2002, this book has become a classic in mathematical finance and has served in numerous courses as a basic textbook and as a basic source and introduction to the field for graduate students and researchers. [...] Altogether this is an extraordinarily well-done book concerning the subjects chosen, with a clear and readable description of its aims and material and a precise and explicit mathematical presentation. [...] This third edition has benefited from some new focus and material and is an enjoyable read and a most relevant textbook." Mathematical Reviews (review of the third edition)
"Since the appearance of the first edition in 2002, this book has become a classic in mathematical finance and has served in numerous courses as a basic textbook and as a basic source and introduction to the field for graduate students and researchers. [...] Altogether this is an extraordinarily well-done book concerning the subjects chosen, with a clear and readable description of its aims and material and a precise and explicit mathematical presentation. [...] This third edition has benefited from some new focus and material and is an enjoyable read and a most relevant textbook." Mathematical Reviews (review of the third edition)