"...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature

The Fractal Geometry of Nature

Efficient Capital Markets: A Review of Theory and Empirical Work Author(s): Eugene F. Fama Source: The Journal of Finance, Vol. 25, No. 2, Papers and Proceedings of the Twenty-Eighth Annual Meeting of the American Finance Association New York, N.Y. December, 28-30, 1969 (May, 1970), pp. 383-417 Published by: Blackwell Publishing for the American Finance Association Stable URL: http://www.jstor.org/stable/2325486 Accessed: 30/03/2010 21:28

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Efficient capital markets: a review of theory and empirical work*

Preface to the Princeton Landmarks in Biology Edition vii Preface xi Symbols Used xiii 1. The Importance of Islands 3 2. Area and Number of Speicies 8 3. Further Explanations of the Area-Diversity Pattern 19 4. The Strategy of Colonization 68 5. Invasibility and the Variable Niche 94 6. Stepping Stones and Biotic Exchange 123 7. Evolutionary Changes Following Colonization 145 8. Prospect 181 Glossary 185 References 193 Index 201

The Theory of Island Biogeography

I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset’s price is important for explaining return skewness and strike-price biases in the BlackScholes (1973) model. The solution technique is based on characteristi c functions and can be applied to other problems.

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A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options

Stochastic Processes

Preface. Elements of Stochastic Processes. Markov Chains. The Basic Limit Theorem of Markov Chains and Applications. Classical Examples of Continuous Time Markov Chains. Renewal Processes. Martingales. Brownian Motion. Branching Processes. Stationary Processes. Review of Matrix Analysis. Index.

A first course in stochastic processes

Stochastic Modeling. Probability Review. The Major Discrete Distributions. @rtant Continuous Distributions. Some Elementary Exercises. Useful Functions, Integrals, and Sums. Conditional Probability and Conditional Expectation: The Discrete Case. The Dice Game Craps. Random Sums. Conditioning on a Continuous Random Variable. Markov Chains: Introduction: Definitions. Transition Probability Matrices of a Markov Chain. Some Markov Chain Models. First Step Analysis. Some Special Markov Chains. Functionals of Random Walks and Success Runs. Another Look at First Step Analysis. The Long Run Behavior of Markov Chains: Regular Transition Probability Matrices. Examples. The Classification of States. The Basic Limit Theorem of Markov Chains. Reducible Markov Chains. Sequential Decisions and Markov Chains. Poisson Processes: The Poisson Distribution and the Poisson Processes. The Law of Rare Events. Distributions Associated with the Poisson Process. The Uniform Distribution and Poisson Processes. Spatial Poisson Processes. Compound and Marked Poisson Processes. Continuous Time Markov Chains: Pure Birth Processes. Ptire Death Processes. Birth and Death Processes. The Limiting Behavior of Birth and Death Processes. Birth and Death Processes with Absorbing States. Finite State Continuous Time Markov Chains. Set Valued Processes. Renewal Phenomena: Definition of a Renewal Process and Related Concepts. Some Examples of Renewal Processes. The Poisson Process Viewed as a Renewal Process. The Asymptotic ]3ehavior as Renewal Process.

An introduction to stochastic modeling

Price changes over a fixed number of transactions may have a Gaussian distribution. Price changes over a fixed time period may follow a stable Paretian distribution, whose variance is infinite. Since the number of transactions in any time period is random, the above statements are not necessarily in disagreement. A possible explanation is proposed by Taylob, and then shown by Mandelbrot to be intimately related to an earlier discussion of the specialists' function of ensuring the continuity of the market.

On the Distribution of Stock Price Differences

We present a probabilistic algorithm for counting the number of unique values in the presence of duplicates. This algorithm has O(q) time complexity, where q is the number of values including duplicates, and produces an estimation with an arbitrary accuracy prespecified by the user using only a small amount of space. Traditionally, accurate counts of unique values were obtained by sorting, which has O(q log q) time complexity. Our technique, called linear counting, is based on hashing. We present a comprehensive theoretical and experimental analysis of linear counting. The analysis reveals an interesting result: A load factor (number of unique values/hash table size) much larger than 1.0 (e.g., 12) can be used for accurate estimation (e.g., 1% of error). We present this technique with two important applications to database problems: namely, (1) obtaining the column cardinality (the number of unique values in a column of a relation) and (2) obtaining the join selectivity (the number of unique values in the join column resulting from an unconditional join divided by the number of unique join column values in the relation to he joined). These two parameters are important statistics that are used in relational query optimization and physical database design.

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Howard M. Taylor

Papers

A first course in stochastic processes

An introduction to stochastic modeling

On the Distribution of Stock Price Differences

A linear-time probabilistic counting algorithm for database applications

Natural selection of life history attributes: an analytical approach.