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基本説明
Extreme value theory (EVT) deals with extreme (rare) events, which are sometimes reported as outliers. This book concentrates on modern topics in EVT, such as processes of exceedances, compound Poisson approximation, Poisson cluster approximation, and nonparametric estimation methods.
Full Description
Extreme value theory (EVT) deals with extreme (rare) events, which are sometimes reported as outliers. Certain textbooks encourage readers to remove outliers—in 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 Finance concentrates 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.
Contents
Methods of Extreme Value Theory. Maximum of Partial Sums. Extremes in Samples of Random Size. Poisson Approximation. Compound Poisson Approximation. Exceedances of Several Levels. Process of Exceedances. Beyond Compound Poisson. Inference on Heavy Tails. Value-at-Risk. Extremal Index. Normal Approximation. Lower Bounds. Appendix. Abbreviations. Bibliography. Index.
