## Introduction to the Mathematics of Finance: From Risk Management To Options PricingThe Mathematics of Finance has become a hot topic in applied mathematics ever since the discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for upper division undergraduate or beginning graduate students in mathematics, finance or economics. With the exception of an optional chapter on the Capital Asset Pricing Model, the book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model. The final chapter is devoted to American options. The mathematics is not watered down but is appropriate for the intended audience. No measure theory is used and only a small amount of linear algebra is required. All necessary probability theory is developed in several chapters throughout the book, on a "need-to-know" basis. No background in finance is required, since the book also contains a chapter on options. The author is Emeritus Professor of Mathematics, having taught at a number of universities, including MIT, UC Santa Barabara, the University of South Florida and the California State University, Fullerton. He has written 27 books in mathematics at various levels and 9 books on computing. His interests lie mostly in the areas of algebra, set theory and logic, probability and finance. When not writing or teaching, he likes to make period furniture, copy Van Gogh paintings and listen to classical music. He also likes tofu. |

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This is a good book. I really liked the way the author introduced probability and statistics then proceeded to introduce financial topics. Then re-visited probability but at a higher level then proceed back into finance. Lots of explanations, not much hand waving and some good examples.

### Contents

VII | 7 |

VIII | 11 |

IX | 15 |

X | 16 |

XI | 20 |

XII | 25 |

XIII | 29 |

XIV | 31 |

LVII | 214 |

LVIII | 217 |

LIX | 219 |

LX | 222 |

LXI | 224 |

LXII | 228 |

LXIII | 233 |

LXIV | 237 |

XV | 36 |

XVI | 41 |

XVII | 46 |

XVIII | 52 |

XIX | 75 |

XX | 79 |

XXIII | 80 |

XXIV | 85 |

XXVI | 89 |

XXVII | 90 |

XXVIII | 92 |

XXIX | 96 |

XXX | 99 |

XXXI | 103 |

XXXII | 104 |

XXXIII | 109 |

XXXIV | 115 |

XXXV | 126 |

XXXVII | 134 |

XXXVIII | 139 |

XXXIX | 141 |

XLI | 144 |

XLII | 148 |

XLIII | 158 |

XLIV | 163 |

XLV | 165 |

XLVI | 167 |

XLVII | 177 |

XLVIII | 182 |

XLIX | 187 |

L | 190 |

LI | 193 |

LII | 195 |

LIII | 200 |

LIV | 203 |

LV | 207 |

LVI | 210 |

LXV | 245 |

LXVI | 248 |

LXVII | 253 |

LXVIII | 258 |

LXIX | 263 |

LXX | 265 |

LXXI | 266 |

LXXII | 270 |

LXXIII | 273 |

LXXIV | 274 |

LXXV | 277 |

LXXVI | 278 |

LXXVIII | 279 |

LXXIX | 280 |

LXXX | 281 |

LXXXI | 282 |

LXXXII | 286 |

LXXXIII | 288 |

LXXXV | 290 |

LXXXVI | 295 |

LXXXVII | 298 |

LXXXVIII | 299 |

LXXXIX | 300 |

XC | 302 |

XCI | 303 |

XCII | 305 |

XCIII | 306 |

XCIV | 315 |

XCV | 318 |

XCVI | 321 |

XCVII | 322 |

XCVIII | 323 |

XCIX | 325 |

C | 331 |

CI | 349 |

351 | |

### Other editions - View all

Introduction to the Mathematics of Finance: From Risk Management to Options ... Steven Roman No preview available - 2011 |

### Common terms and phrases

algebra American option arbitrage Asset Pricing assume attainable alternatives binomial Black-Scholes formula blocks Borel sets Brownian motion process Central Limit Theorem Chapter compute conditional expectation conditional probabilities consider constant convergence convex CRR model defined Definition Let denote density function derivative discounted gain distribution function equation European call example exercise expected return expected value Figure final payoff final value forward contract Hence hyperplane implies independent initial price initial value investor Ke~rT linear functional market portfolio Markowitz martingale measure Mathematics natural probability nonempty nonnegative normal distribution open intervals optimal stopping option pricing formula partition pricing models probability measure probability space profit curve Proof real numbers replicating riskfree asset riskfree rate risky asset sample space self-financing trading strategy selling sequence short position Snell envelop standard normal stochastic process stock price strictly positive strike price subsets supermartingale Suppose Theorem up-tick Var(X variance weights