Stochastic calculus for finance /
Steven E. Shreve.
- 2 volumes : illustrations ; 24 cm.
- Springer finance. Textbook Springer finance .
- Springer finance. Textbook. Springer finance. .
Includes bibliographical references and index.
v. 1. The binomial asset pricing model -- Probability Theory on Coin Toss Space -- State Prices -- American Derivative Securities -- Random Walk -- Interest-Rate-Dependent Assets -- Proof of Fundamental Properties of Conditional Expectations. v. 2. General Probability Theory -- Information and Conditioning -- Brownian Motion -- Stochastic Calculus -- Risk-Neutral Pricing -- Connections with Partial Differential Equations -- Exotic Options -- American Derivative Securities -- Change of Numeraire -- Term Structure Models -- Introduction to Jump Processes -- Advanced Topics in Probability Theory -- Existence of Conditional Expectations -- Completion of Proof of Second Fundamental Theorem of Asset Pricing.
"Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided. The book includes a self-contained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes. This book is being published in two volumes. This second volume develops stochastic calculus, martingales, risk-neutral pricing, exotic options and term structure models, all in continuous time. Masters level students and researchers in mathematical finance and financial engineering will find this book useful." -- Publisher