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Extreme Value Methods with Applications to Finance

Serguei Y. Novak
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2012
Number of Pages: 
373
Format: 
Hardcover
Series: 
Monographs on Statistics and Applied Probability 122
Price: 
99.95
ISBN: 
9781439835746
Category: 
Monograph
We do not plan to review this book.

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

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