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Extreme value methods with applications to finance

Author: Serguei Y Novak
Publisher: Boca Raton, FL : CRC Press, ©2012.
Series: Monographs on statistics and applied probability (Series), 122.
Edition/Format:   Print book : EnglishView all editions and formats
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Document Type: Book
All Authors / Contributors: Serguei Y Novak
ISBN: 9781439835746 1439835748
OCLC Number: 466360875
Description: xxv, 373 pages : illustrations ; 24 cm.
Contents: apt. I Distribution of Extremes --
1. Methods of Extreme Value Theory --
1.1. Order Statistics --
1.2."Blocks" and "Runs" Approaches --
1.3. Method of Recurrent Inequalities --
1.4. Proofs --
2. Maximum of Partial Sums --
2.1. Erdos-Renyi Maximum of Partial Sums --
2.2. Basic Inequalities --
2.3. Limit Theorems for MPS --
2.4. Proofs --
3. Extremes in Samples of Random Size --
3.1. Maximum of a Random Number of r.v.s. --
3.2. Number of Exceedances --
3.3. Length of the Longest Head Run --
3.4. Long Match Patterns --
4. Poisson Approximation --
4.1. Total Variation Distance --
4.2. Method of a Common Probability Space --
4.3. The Stein Method --
4.4. Beyond Bernoulli --
4.5. The Magic Factor --
4.6. Proofs --
5.Compound Poisson Approximation --
5.1. Limit Theory --
5.2. Accuracy of Compound Poisson Approximation --
5.3. Proofs --
6. Exceedances of Several Levels --
6.1. CP Limit Theory --
6.2. General Case --
6.3. Accuracy of Approximation --
6.4. Proofs --
7. Processes of Exceedances --
7.1. One-Level EPPE --
7.2. Excess Process --
7.3.Complete Convergence to CP Processes --
7.4. Proofs --
8. Beyond Compound Poisson --
8.1. Excess Process --
8.2.Complete Convergence --
8.3. Proofs --
pt. II Statistics of Extremes --
9. Inference on Heavy Tails --
9.1. Heavy-Tailed Distribution --
9.2. Estimation Methods --
9.3. Tail Index Estimation --
9.4. Estimation of Extreme Quantiles --
9.5. Estimation of the Tail Probability --
9.6. Proofs --
10. Value-at-Risk --
10.1. Value-at-Risk and Expected Shortfall --
10.2. Traditional Methods of VaR Estimation --
10.3. VaR and ES Estimation from Heavy-Tailed Data --
10.4. VaR over Different Time Horizons --
10.5. Technical Analysis of Financial Data --
10.5.1. Technical versus Fundamental Analyses --
10.5.2. Axioms of the Technical Analysis --
10.5.3. Basic Elliot Waves --
10.5.4. Moving Average --
10.5.5. MACD --
10.5.6. Breakout (Fractal) Signal --
10.5.7. RSI --
10.5.8. TA Tools for Dynamic Risk Measurement --
11. Extremal Index --11.1. Preliminaries --
11.2. Estimation of the Extremal Index --
11.3. Proofs --
12. Normal Approximation --
12.1. Accuracy of Normal Approximation --
12.2. Stein's Method --
12.2.1. Normal Approximation --
12.2.2. Characterization of Smooth Distributions --
12.2.3. Characterization of Discrete Distributions --
12.2.4. Proofs --
12.3. Self-Normalized Sums of Random Variables --
12.3.1. Ratio of Sums of Random Variables --
12.3.2. Student's Statistic --
12.3.3. Proofs --
13. Lower Bounds --
13.1. Preliminary Results --
13.2. Frechet-Rao-Cramer Inequality --
13.3. Information Index --
13.4. Continuity Moduli --
13.5. Tail Index and Extreme Quantiles --
13.6. Proofs --
14. Appendix --
14.1. Probability Distributions --
14.2. Properties of Distributions --
14.3. Probabilistic Identities and Inequalities --
14.4. Distances --
14.5. Large Deviations --
14.6. Elements of Renewal Theory --
14.7. Dependence --
14.8. Point Processes --
14.9. Slowly Varying Functions --
14.10. Useful Identities and Inequalities.
Series Title: Monographs on statistics and applied probability (Series), 122.
Responsibility: Serguei Y. Novak.
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