TY  - BOOK
AU  - Balkema,Guus
AU  - Balkema,Guus
AU  - Embrechts,Paul
TI  - High Risk Scenarios and Extremes: A geometric approach 
T2  - Zurich Lectures in Advanced Mathematics (ZLAM)
SN  - 9783037195352
PY  - 2007///
CY  - Zuerich, Switzerland
PB  - European Mathematical Society Publishing House
KW  - Probability & statistics
KW  - bicssc
KW  - Probability theory and stochastic processes
KW  - msc
KW  - Game theory, economics, social and behavioral sciences
N1  - Restricted to subscribers
N2  - 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 first part is an elegant exposition of coordinatewise extreme  value theory; the second half develops the more basic geometric  theory. Besides a precise mathematical deduction of the main  results, the text yields numerous discussions of a more applied  nature. A twenty page preview introduces the key concepts; the  extensive introduction provides links to financial mathematics and  insurance theory.      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
UR  - https://doi.org/10.4171/035
UR  - http://www.ems-ph.org/img/books/balkema_mini.jpg
ER  -