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Stochastic Calculus for Finance II

Stochastic Calculus for Finance II
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Continuous-Time Models
Steven Shreve
Springer New York
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Artikel-Nr:
9780387401010
Veröffentl:
2004
Einband:
HC runder Rücken kaschiert
Erscheinungsdatum:
03.06.2004
Seiten:
572
Autor:
Steven Shreve
Gewicht:
1016 g
Format:
241x160x37 mm
Serie:
Springer Finance Textbooks
Sprache:
Englisch
Beschreibung:

Steven E. Shreve is Co-Founder of the Carnegie Mellon MS Program in Computational Finance and winner of the Carnegie Mellon Doherty Prize for sustained contributions to education.

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.

Master's level studentsand researchers in mathematical finance and financial engineering will find this book useful.

This text has grown out of a two-semester course sequence in the Carnegie Mellon Master's program in Computational Finance. It contains numerous examples, exercises, and references. It assumes the reader is familiar with differential and integral calculus and basic concepts from calculus-based probability. It does not assume familiarity with measure-theoretic probability, but rather informally develops the necessary tools from this subject within the text.
1 General Probability Theory.- 2 Information and Conditioning.- 3 Brownian Motion.- 4 Stochastic Calculus.- 5 Risk-Neutral Pricing.- 6 Connections with Partial Differential Equations.- 7 Exotic Options.- 8 American Derivative Securities.- 9 Change of Numéraire.- 10 Term-Structure Models.- 11 Introduction to Jump Processes.- A Advanced Topics in Probability Theory.- A.1 Countable Additivity.- A.3 Random Variable with Neither Density nor Probability Mass Function.- B Existence of Conditional Expectations.- C Completion of the Proof of the Second Fundamental Theorem of Asset Pricing.- References.

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