Stochastic finance

"This comprehensive text presents an introduction to pricing and hedging in financial models, with an emphasis on analytical and probabilistic methods. It demonstrates both the power and limitations of mathematical models in finance. The book starts with the basics of finance and stochastic calculus and builds up to special topics, such as options, derivatives, and credit default and jump processes. Many real examples illustrate the topics and classroom-tested exercises are included in each chapter, with selected solutions at the back of the book"-- "Preface This text is an introduction to pricing and hedging in discrete and continuous time financial models without friction (i.e. without transaction costs), with an emphasis on the complementarity between analytical and probabilistic methods. Its contents are mostly mathematical, and also aim at making the reader aware of both the power and limitations of mathematical models in finance, by taking into account their conditions of applicability. The book covers a wide range of classical topics including Black-Scholes pricing, exotic and american options, term structure modeling and change of num eraire, as well as models with jumps. I