An Elementary Introduction to Mathematical Finance

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Cambridge University Press, Feb 28, 2011 - Mathematics
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This textbook on the basics of option pricing is accessible to readers with limited mathematical training. It is for both professional traders and undergraduates studying the basics of finance. Assuming no prior knowledge of probability, Sheldon M. Ross offers clear, simple explanations of arbitrage, the Black-Scholes option pricing formula, and other topics such as utility functions, optimal portfolio selections, and the capital assets pricing model. Among the many new features of this third edition are new chapters on Brownian motion and geometric Brownian motion, stochastic order relations and stochastic dynamic programming, along with expanded sets of exercises and references for all the chapters.
 

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Contents

Probability
1
Normal Random Variables
22
Brownian Motion and Geometric Brownian Motion
34
Interest Rates and Present Value Analysis
48
Pricing Contracts via Arbitrage
73
The Arbitrage Theorem
92
The BlackScholes Formula
106
Additional Results on Options
131
Stochastic Order Relations
193
Optimization Models
212
Stochastic Dynamic Programming
228
Exotic Options
247
Beyond Geometric Brownian Motion Models
265
Autoregressive Models and Mean Reversion
285
Index
303
Copyright

Valuing by Expected Utility
165

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About the author (2011)

Sheldon M. Ross is the Epstein Chair Professor at the Department of Industrial and Systems Engineering, University of Southern California. He received his Ph.D. in statistics at Stanford University in 1968 and was formerly a Professor at the University of California, Berkeley, from 1976 until 2004. He has published more than 100 articles and a variety of textbooks in the areas of statistics and applied probability, including Topics in Finite and Discrete Mathematics (2000), Introduction to Probability and Statistics for Engineers and Scientists, 4th edition (2009), A First Course in Probability, 8th edition (2009), and Introduction to Probability Models, 10th edition (2009), among others. Dr Ross serves as the editor for Probability in the Engineering and Informational Sciences.

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