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 periodArbitrage theoryPreferencesOptimality and equilibriumMonetary measures of riskPart II Dynamic hedgingDynamic arbitrage theoryAmerican contingent claimsSuperhedgingEfficient hedgingHedging under constraintsMinimizing the hedging errorDynamic risk measures 4th revised edition Includes exercises and tips for solutions Suitable for students researchers and practitioners

Stochastic Finance PDF

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