Fueled in part by some extraordinary theoretical developments in finance, an explosive growth of information and computing technology, and the global expansion of investment activity, investment theory currently commands a high level of intellectual attention. Recent developments in the field are being infused into university classrooms, financial service organizations, business ventures, and into the awareness of many individual investors. Modern investment theory using the language of mathematics is now an essential aspect of academic and practitioner training.

Representing a breakthrough in the organization of finance topics, Investment Science will be an indispensable tool in teaching modern investment theory. It presents sound fundamentals and shows how real problems can be solved with modern, yet simple, methods. David Luenberger gives thorough yet highly accessible mathematical coverage of standard and recent topics of introductory investments: fixed-income securities, modern portfolio theory and capital asset pricing theory, derivatives (futures, options, and swaps), and innovations in optimal portfolio growth and valuation of multiperiod risky investments. Throughout the book, he uses mathematics to present essential ideas of investments and their applications in business practice. The creative use of binomial lattices to formulate and solve a wide variety of important finance problems is a special feature of the book.

In moving from fixed-income securities to derivatives, Luenberger increases naturally the level of mathematical sophistication, but never goes beyond algebra, elementary statistics/probability, and calculus. He includes appendices on probability and calculus at the end of the book for student reference. Creative examples and end-of-chapter exercises are also included to provide additional applications of principles given in the text.

Ideal for investment or investment management courses in finance, engineering economics, operations research, and management science departments, Investment Science has been successfully class-tested at Boston University, Stanford University, and the University of Strathclyde, Scotland, and used in several firms where knowledge of investment principles is essential. Executives, managers, financial analysts, and project engineers responsible for evaluation and structuring of investments will also find the book beneficial. The methods described are useful in almost every field, including high-technology, utilities, financial service organizations, and manufacturing companies.

"This is the best single volume on investments ever written. It is one of the only books to cover both derivatives and portfolio optimization, and it does not get bogged down with unnecessary notation. It is a real page turner. For non-finance types looking for a serious, rigorous introduction to the subject, look no further."--Wayne Winston, Professor of Decision Sciences, Indiana University

"This book is well written, clear, and cohesive. There is not a single investment textbook that I am aware of that gives such in-depth and organized treatment of the topics chosen by this book. A distinguishing feature is that it gives you every single detail and tool that you would ever need to solve problems."--Raymond Kan, University of Toronto

"Investment Science is a wonderful textbook treatment of investment theory for the quantitatively-minded undergraduate or masters student. This book is typical of David Luenberger's uncanny way of simplifying complex technical material without loss of rigor. He divides and conquers the subject, starting with the basics of simple fixed-income securities, and building up to the valuation and hedging of derivative securities in a dynamic setting under uncertainty. There is a lovely interplay of arbitrage calculations, portfolio selection for individual investors, and market equilibrium. The book will be especially valuable for those entering the subject from other quantitative fields."--Darrell Duffie, Stanford University Graduate School of Business

"Options and continuous-time finance are important enough to warrant a whole course in MBA programs. David Luenberger's book makes continuous time finance accessible to any student who has mastered elementary calculus and probability theory, and motivates the subject by using it to solve a broad range of option-type problems relating to stock, bond, and commodity markets."--Jack Treynor, President, Treynor Capital Management, Inc.

"This textbook takes a refreshing approach to the science of investing. It is extremely well-written. Financial principles and ideas are laid out clearly and in an orderly fashion." — Joseph Cherian, Department of Finance, School of Management, Boston University

"The book is very clearly written and introduces advanced concepts (e.g. duration and convexity of bonds) in relatively simple and intuitive ways early in the book. There are lots of carefully thought out examples to illustrate important points and applications of particular methodologies. Overall, the book does a great job of taking a reader who knows essentially nothing about finance from very basic concepts up through rather advanced valuation topics."--James E. Hodder, University of Wisconsin-Madison

"This text is a breakthrough in the organization of very important theory."--Lloyd Nirenberg, Director, Business Development, National Semiconductor Corp.

"This book provides great insights and practical approaches for anyone interested in the relation between markets and decisions. It is written in a unique and creative manner." --Nick V. Arvanitidis, CEO,IDEA GmbH., and Former CEO, Sequus Pharmaceuticals

"Luenberger's book is very informative and offers genuinely new insights into important investment problems."--Paul McEntire, Chairman, Skye Investment Advisors LLC

"Professor Luenberger's book, particularly Chapters 15 &16, lays the foundation for the analytic approach Enron takes when assessing and managing risk in its non-traded asset portfolio."--Andrea Vail, Vice President, Enron Capital Management

Unlike its predecessors, this systematic survey of the law of Athens is based on explicit discussion of how the subject might be studied, incorporating topics like the democratic political system and social structure. The author draws primarily on the surviving law-court speeches of the Attic

orators, but also uses Athenian comedy, public inscriptions, and various historical and philosophical texts. Technical and legal terms, ancient and modern, are explained in a comprehensive glossary.

David G. Luenberger, Professor in Engineering-Economics SystemsandOperations Research, Stanford University. He has written several successful books with Addison-Wesley and John Wiley publishers.

1. Introduction

1.1. Cash Flows

1.2. Investments and Markets

1.3. Typical Investment Problems

1.4. Organization of the Book

I. Deterministic Cash Flow Streams

2. The Basic Theory of Interest

2.1. Principal and Interest

2.2. Present Value

2.3. Present and Future Values of Streams

2.4. Internal Rate of Return

2.5. Evaluation Criteria

2.6. Applications and Extensions

2.7. Summary

2.8. Exercises

3. Fixed-Income Securities

3.1. The Market for Future Cash

3.2. Value Formulas

3.3. Bond Details

3.4. Yield

3.5. Duration

3.6. Immunization

3.7. Convexity

3.8. Summary

3.9. Exercises

4. The Term Structure of Interest Rates

4.1. The Yield Curve

4.2. The Term Structure

4.3. Forward Rates

4.4. Term Structure Explanations

4.5. Expectation Dynamics

4.6. Running Present Value

4.7. Floating Rate Bonds

4.8. Duration

4.9. Immunization

4.10. Summary

4.11. Exercises

5. Applied Interest Rate Analysis

5.1. Capital Budgeting

5.2. Optimal Portfolios

5.3. Dynamic Cash Flow Processes

5.4. Optimal Management

5.5. The Harmony Theorem

5.6. Valuation of a Firm

5.7. Summary

5.8. Exercises

II. Single-Period Random Cash Flows

6. Mean-Variance Portfolio Theory

6.1. Asset Return

6.2. Random Variables

6.3. Random Returns

6.4. Portfolio Mean and Variance

6.5. The Feasible Set

6.6. The Markowitz Model

6.7. The Two-Fund Theorem

6.8. Inclusion of a Risk-Free Asset

6.9. The One-Fund Theorem

6.10. Summary

6.11. Exercises

7. The Capital Asset Pricing Model

7.1. Market Equilibrium

7.2. The Capital Market Line

7.3. The Pricing Model

7.4. The Security Market Line

7.5. Investment Implications

7.6. Performance Evaluation

7.7. CAPM as a Pricing Formula

7.8. Project Choice

7.9. Summary

7.10. Exercises

8. Models and Data

8.1. Introduction

8.2. Factor Models

8.3. The CAPM as a Factor Model

8.4. Arbitrage Pricing Theory

8.5. Data and Statistics

8.6. Estimation of Other Parameters

8.7. Tilting Away from Equilibrium

8.8. A Multiperiod Fallacy

8.9. Summary

8.10. Exercises

9. General Principles

9.1. Introduction

9.2. Utility Functions

9.3. Risk Aversion

9.4. Specification of Utility Functions

9.5. Utility Functions and the Mean-Variance Criterion

9.6. Linear Pricing

9.7. Portfolio Choice

9.8. Log-Optimal Pricing

9.9. Finite State Models

9.10. Risk-Neutral Pricing

9.11. Pricing Alternatives

9.12. Summary

9.13. Exercises

III. Derivative Securities

10. Forwards, Futures, and Swaps

10.1. Introduction

10.2. Forward Contracts

10.3. Forward Prices

10.4. The Value of a Forward Contract

10.5. Swaps

10.6. Basics of Futures Contracts

10.7. Futures Prices

10.8. Relation to Expected Spot Price

10.9. The Perfect Hedge

10.10. The Minimum-Variance Hedge

10.11. Optimal Hedging

10.12. Hedging Nonlinear Risk

10.13. Summary

10.14. Exercises

11. Models of Asset Dynamics

11.1. Binominal Lattice Model

11.2. The Additive Model

11.3. The Multiplicative Model

11.4. Typical Parameter Values

11.5. Lognormal Random Variables

11.6. Random Walks and Wiener Processes

11.7. A Stock Price Process

11.8. Ito's Lemma

11.9. Binomial Lattice Revisited

11.10. Summary

11.11. Exercises

11.12. References

12. Basic Options Theory

12.1. Option Concepts

12.2. The Nature of Option Value

12.3. Option Combinations and Put-Call Parity

12.4. Early Exercise

12.5. Single-Period Binomial Options Theory

12.6. Multiperiod Options

12.7. More General Binomial Problems

12.8. Evaluating Real Investment Opportunities

12.9. General Risk-Neutral Pricing

12.10. Summary

12.11. Exercises

12.12. References

13. Additional Options Topics

13.1. Introduction

13.2. The Black-Scholes Equation

13.3. Call Option Formula

13.4. Risk-Neutral Valuation

13.5. Delta

13.6. Replication, Synthetic Options, and Portfolio Insurance/st

13.7. Computational Methods

13.8. Exotic Options

13.9. Storage Costs and Dividends

13.10. Martingale Pricing

13.11. Summary

13.12. Exercises

13.13. References

14. Interest Rate Derivatives

14.1. Examples of Interest-Rate Derivatives

14.2. The Need for a Theory

14.3. The Binomial Approach

14.4. Pricing Applications

14.5. Leveling and Adjustable-Rate Loans

14.6. The Forward Equation

14.7. Matching the Term Structure

14.8. Immunization

14.9. Collateralized Mortgage Obligations

14.10. Models of Interest Rate Dynamics

14.11. Continuous-Time Solutions

14.12. Summary

14.13. Exercises

14.14. References

IV. General Cash Flow Streams

15. Optimal Portfolio Growth

15.1. The Investment Wheel

15.2. The Log Utility Approach to Growth

15.3. Properties of the Log-Optimal Strategy

15.4. Alternative Approaches

15.5. Continuous-Time Growth

15.6. The Feasible Region

15.7. The Log-Optimal Pricing Formula

15.8. Log-Optimal Pricing and the Black-Scholes Equation

15.9. Summary

15.10. Exercises

15.11. References

16. General Investment Evaluation

16.1. Multiperiod Securities

16.2. Risk-Neutral Pricing

16.3. Optimal Pricing

16.4. The Double Lattice

16.5. Pricing in a Double Lattice

16.6. Investments with Private Uncertainty

16.7. Buying Price Analysis

16.8. Continuous-Time Evaluation

16.9. Summary

16.10. Exercises

16.11. References

A. Basic Probability Theory

A.1. General Concepts

A.2. Normal Random Variables

A.3. Lognormal Random Variables

B. Calculus and Optimization

B.1. Functions

B.2. Differential Calculus

B.3. Optimization