Extreme Value Methods ith Applications to Finance [Hardcover]

Extreme value theory (EVT) deals with extreme (rare) events, which are sometimes reported as outliers. Certain textbooks encourage readers to remove outliersin other words, to correct reality if it does not fit the model. Recognizing that any model is only an approximation of reality, statisticians are eager to extract information about unknown distribution making as few assumptions as possible.

Extreme Value Methods with Applications to Financeconcentrates on modern topics in EVT, such as processes of exceedances, compound Poisson approximation, Poisson cluster approximation, and nonparametric estimation methods. These topics have not been fully focused on in other books on extremes. In addition, the book covers:

• Extremes in samples of random size
• Methods of estimating extreme quantiles and tail probabilities
• Self-normalized sums of random variables
• Measures of market risk

Along with examples from finance and insurance to illustrate the methods, Extreme Value Methods with Applications to Finance includes over 200 exercises, making it useful as a reference book, self-study tool, or comprehensive course text.

A systematic background to a rapidly growing branch of modern Probability and Statistics: extreme value theory for stationary sequences of random variables.

Introduction

Distribution of Extremes

Methods of Extreme Value Theory
Order Statistics
Blocks and Runs Approaches
Method of Recurrent Inequalities
Proofs

Maximum of Partial Sums
ErdQsR?nyi Maximum of Partial Sums
Basic Inequalities
Limit Theorems for MPS
Proofs

Extremes in Samplelƒš