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Document Details :

Title: Tail Variance Premium with Applications for Elliptical Portfolio of Risks
Author(s): FURMAN, Edward , LANDSMAN, Zinoviy
Journal: ASTIN Bulletin
Volume: 36    Issue: 2   Date: 2006   
Pages: 433-462
DOI: 10.2143/AST.36.2.2017929

Abstract :
In this paper we consider the important circumstances involved when risk managers
are concerned with risks that exceed a certain threshold. Such conditions
are well-known to insurance professionals, for instance in the context of policies
involving deductibles and reinsurance contracts. We propose a new premium
called tail variance premium (TVP) which answers the demands of these circumstances.
In addition, we suggest a number of risk measures associated with
TVP. While the well-known tail conditional expectation risk measure provides
a risk manager with information about the average of the tail of the loss
distribution, tail variance risk measure (TV) estimates the variability along such
a tail. Furthermore, given a multivariate setup, we offer a number of allocation
techniques which preserve different desirable properties (sub-additivity and fulladditivity,
for instance). We are able to derive explicit expressions for TV and
TVP, and risk capital decomposition rules based on them, in the general framework
of multivariate elliptical distributions. This class is very popular among
actuaries and risk managers because it contains distributions with marginals
whose tails are heavier than those of normal distributions. This distinctive feature
is desirable when modeling financial datasets. Moreover, according to our
results, in some cases there exists an optimal threshold, such that by choosing
it, an insurance company minimizes its risk.