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Guus Balkema (University of Amsterdam, The Netherlands)
Paul Embrechts (ETH Zurich, Switzerland)
High Risk Scenarios and Extremes
A geometric approachISBN print 978-3-03719-035-7, ISBN online 978-3-03719-535-2
DOI 10.4171/035
September 2007, 389 pages, softcover, 17.0 x 24.0 cm.
48.00 Euro
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.
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