Mathematical Finance and Probability: A Discrete Introduction

✍ Scribed by Pablo Koch Medina, Sandro Merino (auth.)

• Publisher: Birkhäuser Basel
• Year: 2003
• Tongue: English
• Leaves: 325
• Edition: 1
• Category: Library

✦ Synopsis

The objective of this book is to give a self-contained presentation to the theory underlying the valuation of derivative financial instruments, which

is becoming a standard part of the toolbox of professionals in the financial industry. Although a complete derivation of the Black-Scholes

option pricing formula is given, the focus is on finite-time models. Not going for the greatest possible level of generality is greatly rewarded by

a greater insight into the underlying economic ideas, putting the reader in an excellent position to proceed to the more general continuous-time

theory.

The material will be accessible to students and practitioners having a working knowledge of linear algebra and calculus. All additional material

is developed from the very beginning as needed. In particular, the book also offers an introduction to modern probability theory, albeit mostly

within the context of finite sample spaces.

The style of presentation will appeal to financial economics students seeking an elementary but rigorous introduction to the subject; mathematics

and physics students looking for an opportunity to become acquainted with this modern applied topic; and mathematicians, physicists or quantitatively inclined economists working in the financial industry.

✦ Table of Contents

Front Matter....Pages i-ix
Introduction....Pages 1-6
A Short Primer on Finance....Pages 7-39
Positive Linear Functionals....Pages 41-72
Finite Probability Spaces....Pages 73-87
Random Variables....Pages 89-109
General One-Period Models....Pages 111-128
Information and Randomness....Pages 129-145
Independence....Pages 147-160
Multi-Period Models:The Main Issues....Pages 161-177
Conditioning and Martingales....Pages 179-190
The Fundamental Theorems of Asset Pricing....Pages 191-199
The Cox—Ross—Rubinstein Model....Pages 201-219
The Central Limit Theorem....Pages 221-246
The Black—Scholes Formula....Pages 247-255
Optimal Stopping....Pages 257-275
American Claims....Pages 277-295
Back Matter....Pages 297-328

✦ Subjects

Quantitative Finance; Probability Theory and Stochastic Processes