Optimal approximations for risk measures of sums of lognormals based on conditional expectations

Steven Vanduffel, Xianling Chen, Jan Dhaene, Marc Goovaerts, Luc Henrard, Rob Kaas

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

In this paper we investigate approximations for the distribution function of
a sum S of lognormal random variables. These approximations are obtained
by considering the conditional expectation E[S | ] of S with respect to a
conditioning random variable .
The choice for is crucial in order to obtain accurate approximations. The
different alternatives for that have been proposed in literature to date are
'global' in the sense that is chosen such that the entire distribution of the
approximation E[S | ] is 'close' to the corresponding distribution of the original
sum S.
In an actuarial or a financial context one is often only interested in a particular
tail of the distribution of S. Therefore in this paper we propose approximations
E[S | ] which are only locally optimal, in the sense that the relevant tail of
the distribution of E[S | ] is an accurate approximation for the corresponding
tail of the distribution of S. Numerical illustrations reveal that local optimal
choices for can improve the quality of the approximations in the relevant tail
significantly.
We also explore asymptotic properties of the approximations E[S | ] and
investigate links with results from Asmussen & Royas-Nandayapa (2005). Finally,
we briefly adress the sub-optimality of Asian options from the point of view of
risk averse decision makers with a fixed investment horizon.
Original languageEnglish
Pages (from-to)202-218
Number of pages17
JournalJournal of Computational and Applied Mathematics
Volume221
Issue number1
Publication statusPublished - 2008

Keywords

  • comonotonicity

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