Introduction to the Mathematics of Finance : From Risk Management to Options Pricing / by Steven Roman
(Undergraduate Texts in Mathematics)
| データ種別 | 電子ブック |
|---|---|
| 出版情報 | New York, NY : Springer New York : Imprint: Springer , 2004 |
| 本文言語 | 英語 |
| 大きさ | XV, 356 p : online resource |
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| 内容注記 | Portfolio Risk Management Option Pricing Models Assumptions Arbitrage Probability I: An Introduction to Discrete Probability 1.1 Overview 1.2 Probability Spaces 1.3 Independence 1.4 Binomial Probabilities 1.5 Random Variables 1.6 Expectation 1.7 Variance and Standard Deviation 1.8 Covariance and Correlation; Best Linear Predictor Exercises Portfolio Management and the Capital Asset Pricing Model 2.1 Portfolios, Returns and Risk 2.2 Two-Asset Portfolios 2.3 Multi-Asset Portfolios Exercises Background on Options 3.1 Stock Options 3.2 The Purpose of Options 3.3 Profit and Payoff Curves 3.4 Selling Short Exercises An Aperitif on Arbitrage 4.1 Background on Forward Contracts 4.2 The Pricing of Forward Contracts 4.3 The Put-Call Option Parity Formula 4.4 Option Prices Exercises Probability II: More Discrete Probability 5.1 Conditional Probability 5.2 Partitions and Measurability 5.3 Algebras 5.4 Conditional Expectation 5.5 Stochastic Processes 5.6 Filtrations and Martingales Exercises Discrete-Time Pricing Models 6.1 Assumptions 6.2 Positive Random Variables 6.3 The Basic Model by Example 6.4 The Basic Model 6.5 Portfolios and Trading Strategies 6.6 The Pricing Problem: Alternatives and Replication 6.7 Arbitrage Trading Strategies 6.8 Admissible Arbitrage Trading Strategies 6.9 Characterizing Arbitrage 6.10 Computing Martingale Measures Exercises The Cox-Ross-Rubinstein Model 7.1 The Model 7.2 Martingale Measures in the CRR model 7.3 Pricing in the CRR Model 7.4 Another Look at the CRR Model via Random Walks Exercises Probability III: Continuous Probability 8.1 General Probability Spaces 8.2 Probability Measures on ? 8.3 Distribution Functions 8.4 Density Functions 8.5 Types of Probability Measures on ? 8.6 Random Variables 8.7 The Normal Distribution 8.8 Convergence in Distribution 8.9 The Central Limit Theorem Exercises The Black-Scholes Option Pricing Formula 9.1 Stock Prices and Brownian Motion 9.2 The CRR Model in the Limit: Brownian Motion 9.3 Taking the Limit as °t ? 0 9.4 The Natural CRR Model 9.5 The Martingale Measure CRR Model 9.6 More on the Model From a Different Perspective: Ito's Lemma 9.7 Are the Assumptions Realistic? 9.8 The Black-Scholes Option Pricing Formula 9.9 How Black-Scholes is Used in Practice: Volatility Smiles and Surfaces 9.10 How Dividends Affect the Use of Black-Scholes Exercises Optimal Stopping and American Options 10.1 An Example 10.2 The Model 10.3 The Payoffs 10.4 Stopping Times 10.5 Stopping the Payoff Process 10.6 The Stopped Value of an American Option 10.7 The Initial Value of an American Option, or What to Do At Time to 10.8 What to Do At Time tk 10.9 Optimal Stopping Times and the Snell Envelop 10.10 Existence of Optimal Stopping Times 10.11 Characterizing the Snell Envelop 10.12 Additional Facts About Martingales 10.13 Characterizing Optimal Stopping Times 10.14 Optimal Stopping Times and the Doob Decomposition 10.15 The Smallest Optimal Stopping Time 10.16 The Largest Optimal Stopping Time Exercises Appendix A: Pricing Nonattainable Alternatives in an Incomplete Market A. 1 Fair Value in an Incomplete Market A.2 Mathematical Background A.3 Pricing Nonattainable Alternatives Exercises Appendix B: Convexity and the Separation Theorem B. 1 Convex, Closed and Compact Sets B.2 Convex Hulls B.3 Linear and Affine Hyperplanes B.4 Separation Selected Solutions References |
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| 一般注記 | The 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 |
| 著者標目 | *Roman, Steven author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Finance LCSH:Economics, Mathematical LCSH:Probabilities FREE:Mathematics FREE:Quantitative Finance FREE:Probability Theory and Stochastic Processes FREE:Finance, general |
| 分 類 | DC23:519 |
| 巻冊次 | ISBN:9781441990051 
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| ISBN | 9781441990051 |
| URL | http://dx.doi.org/10.1007/978-1-4419-9005-1 |
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