(Not in Extreme Value Methods with Applications to Finance
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$99.95$89.96 - Hardback: 399 pages
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- Published: December 2011
- ISBN: 978-1-4398357-4-6
- Publisher: CRC Press
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- By Serguei Y. Novak.
Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability.
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.
Table of Contents
Introduction
Distribution of Extremes
Methods of Extreme Value Theory
Order Statistics
"Blocks" and "Runs" Approaches
Method of Recurrent Inequalities
Proofs
Maximum of Partial Sums
Erdős–Rényi Maximum of Partial Sums
Basic Inequalities
Limit Theorems for MPS
Proofs
Extremes in Samples of Random Size
Maximum of a Random Number of r.v.s
Number of Exceedances
Length of the Longest Head Run
Long Match Patterns
Poisson Approximation
Total Variation Distance
Method of a Common Probability Space
The Stein Method
Beyond Bernoulli
The Magic Factor
Proofs
Compound Poisson Approximation
Limit Theory
Accuracy of CP Approximation
Proofs
Exceedances of Several Levels
CP Limit Theory
General Case
Accuracy of Approximation
Proofs
Processes of Exceedances
One-level EPPE
Excess Process
Complete Convergence to CP Processes
Proofs
Beyond Compound Poisson
Excess Process
Complete Convergence
Proofs
Statistics of Extremes
Inference on Heavy Tails
Heavy-tailed distributions
Estimation Methods
Tail Index Estimation
Estimation of Extreme Quantiles
Estimation of the Tail Probability
Proofs
Value-at-Risk.
Value-at-Risk and Expected Shortfall
Traditional Methods of VaR Estimation
VaR and ES Estimation from Heavy-Tailed Data
VaR over Different Time Horizons
Technical Analysis of Financial Data
Extremal Index
Preliminaries
Estimation of the Extremal Index
Proofs
Normal Approximation.
Accuracy of Normal Approximation
Stein’s Method
Self-Normalized Sums of r.v.s
Proofs
Lower Bounds
Preliminary Results
Fréchét–Rao–Cramér Inequality
Information Index
Continuity Moduli
Tail Index and Extreme Quantiles
Proofs
Appendix
Probability Distributions
Properties of Distributions
Probabilistic Identities and Inequalities
Distances
Large Deviations
Elements of Renewal Theory
Dependence
Point Processes
Slowly Varying Functions
Useful Identities and Inequalities
References
Index
Author/Editor Biography
Dr S.Y. Novak earned his Ph.D. at the Novosibirsk Institute of Mathematics under the supervision of Dr S.A. Utev in 1988. The Novosibirsk group forms a part of Russian tradition in Probability & Statistics that extends its roots to Kolmogorov and Markov.
Dr S.Y. Novak began his teaching carrier at the Novosibirsk Electrotechnical Institute (NETI) and Novosibirsk Institute of Geodesy, held post-doctoral positions at the University of Sussex and Eurandom (Technical University of Eindhoven), and taught at Brunel University in West London, before joining the Middlesex University (London) in 2003. He published over 40 papers, mostly on the topic of Extreme Value Theory, in which he is considered an expert.
