@article { ISI:000345588000005,
	title = {The effect of aggregation on extremes from asymptotically independent light-tailed risks},
	journal = {EXTREMES},
	volume = {17},
	number = {4},
	year = {2014},
	month = {DEC},
	pages = {615-631},
	publisher = {SPRINGER},
	type = {Article},
	address = {233 SPRING ST, NEW YORK, NY 10013 USA},
	abstract = {Portfolio risk diversification is a well established concept in finance. While aggregation of several risky assets generally reduces the overall investment risk due to diversification, the effectiveness of diversification depends on the stochastic behaviour of the returns of the assets comprising the portfolio. The paper proposes a new approach to quantifying the effect of portfolio tail diversification by looking at the asymptotic behaviour of the ratio of the largest loss on the portfolio to the sum of the largest losses on the individual investments held on the stand-alone basis. It is assumed that independent and identically distributed random vectors from the underlying distribution, describing the behaviour of returns on the assets in the portfolio, can be scaled to converge onto a deterministic limit set. This property is satisfied by a number of distributions commonly used in finance. Several analytical examples are given to illustrate the proposed asymptotic diversification index as a measure of the effect of risk aggregation on extremes as well as to quantify the impact of dimension on the diversification and as a tool in optimal portfolio selection.},
	keywords = {Asymptotic independence, Light-tailed distributions, Limit set, Risk diversification, Tail risk, Weak tail dependence coefficient},
	issn = {1386-1999},
	doi = {10.1007/s10687-014-0192-y},
	author = {Nolde, Natalia}
}
@article { ISI:000327908200006,
	title = {Geometric interpretation of the residual dependence coefficient},
	journal = {JOURNAL OF MULTIVARIATE ANALYSIS},
	volume = {123},
	year = {2014},
	month = {JAN},
	pages = {85-95},
	publisher = {ELSEVIER INC},
	type = {Article},
	address = {525 B STREET, STE 1900, SAN DIEGO, CA 92101-4495 USA},
	abstract = {The residual dependence coefficient was originally introduced by Ledford and Tawn (1996) [25] as a measure of residual dependence between extreme values in the presence of asymptotic independence. We present a geometric interpretation of this coefficient with the additional assumptions that the random samples from a given distribution can be scaled to converge onto a limit set and that the marginal distributions have Weibull-type tails. This result leads to simple and intuitive computations of the residual dependence coefficient for a variety of distributions. (C) 2013 Elsevier Inc. All rights reserved.},
	keywords = {Asymptotic independence, Geometric approach, Limit set, Multivariate density, Residual dependence coefficient, Sample clouds},
	issn = {0047-259X},
	doi = {10.1016/j.jmva.2013.08.018},
	author = {Nolde, Natalia}
}
@article { ISI:000278796800008,
	title = {ASYMPTOTIC INDEPENDENCE FOR UNIMODAL DENSITIES},
	journal = {ADVANCES IN APPLIED PROBABILITY},
	volume = {42},
	number = {2},
	year = {2010},
	month = {JUN},
	pages = {411-432},
	publisher = {APPLIED PROBABILITY TRUST},
	type = {Article},
	address = {THE UNIVERSITY, SCHOOL MATHEMATICS STATISTICS, SHEFFIELD S3 7RH, ENGLAND},
	abstract = {Asymptotic independence of the components of random vectors is a concept used in many applications. The standard criteria for checking asymptotic independence are given in terms of distribution functions (DFs). DFs are rarely available in an explicit form, especially in the multivariate case. Often we are given the form of the density or, via the shape of the data clouds, we can obtain a good geometric image of the asymptotic shape of the level sets of the density. In this paper we establish a simple sufficient condition for asymptotic independence for light-tailed densities in terms of this asymptotic shape. This condition extends Sibuya{\textquoteright}s classic result on asymptotic independence for Gaussian densities.},
	keywords = {Asymptotic independence, blunt, homothetic density, level set, skew normal, star shaped},
	issn = {0001-8678},
	author = {Balkema, Guus and Nolde, Natalia}
}
