High risk scenarios and extremes : a geometric approach / Guus Balkema, Paul Embrechts.

Format:

Book

Author/Creator:

Balkema, A. A.

Contributor:

Embrechts, Paul, 1953-

Rosengarten Family Fund.

Series:

Zurich lectures in advanced mathematics

Language:

English

Subjects (All):

Multivariate analysis.

Extreme value theory.

Point processes.

Risk assessment--Mathematical models.

Risk assessment.

Multivariate Analysis.

Medical Subjects:

Multivariate Analysis.

Physical Description:

xiii, 375 pages ; 24 cm.

Place of Publication:

Amsterdam : European Mathematical Society, ©2007.

Summary:

"Quantitative Risk Management (QRM) has become a field of research of considerable importance to numerous areas of application, including insurance, banking, energy, medicine, reliability. Mainly motivated by examples from insurance and finance, the authors develop a theory for handling multivariate extremes. The approach borrows ideas from portfolio theory and aims at an intuitive approach in the spirit of the Peaks over Thresholds method. The point of view is geometric. It leads to a probabilistic description of what in QRM language may be referred to as a high risk scenario: the conditional behaviour of risk factors given that a large move on a linear combination [portfolio, say] has been observed. The theoretical models which describe such conditional extremal behaviour are characterized and their relation to the limit theory for coordinatewise maxima is explained." "The book is based on a graduate course on point processes and extremes. It could form the basis for an advanced course on multivariate extreme value theory or a course on mathematical issues underlying risk. Students in statistics and finance with a mathematical, quantitative background are the prime audience. Actuaries and risk managers involved in data based risk analysis will find the models discussed in the book stimulating. The text contains many indications for further research."--Jacket.

Contents:

Preview

A recipe

Contents

Notation

I. Point Processes

1. An intuitive approach

2. Poisson point processes

3. The distribution

4. Convergence

5. Converging sample clouds

II. Maxima

6. The univariate theory: maxima and exceedances

7. Componentwise maxima

III. High Risk Limit Laws

8. High risk scenarios

9. The Gauss-exponential domain, rotund sets

10. The Gauss-exponential domain, unimodal distributions

11. Flat functions and flat measures

12. Heavy tails and bounded vectors

13. The multivariate GPDs

IV. Thresholds

14. Exceedances over horizontal thresholds

15. Horizontal thresholds

examples

16. Heavy tails and elliptic thresholds

17. Heavy tails

18. Regular variation and excess measures

V. Open problems

19. The stochastic model

20. The statistical analysis.

Notes:

Includes bibliographical references (pages (361-368) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Rosengarten Family Fund.

ISBN:

9783037190357

3037190353

OCLC:

191922927

Publisher Number:

9783037190357