Conditional tail moments of the exponential family and its related distributions

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The risk measure is a central theme in the risk management literature. For good reasons, the conditional tail expectation (CTE) has received much interest in both insurance and finance applications. It provides for a measure of the expected riskiness in the tail of the loss distribution. In this article we derive explicit formulas of the CTE and higher moments for the univariate exponential family class, which extends the natural exponential family, using the canonical representation. In addition we show how to compute the conditional tail expectations of other related distributions using transformation and conditioning. Selected examples are presented for illustration, including the generalized Pareto and generalized hyperbolic distributions. We conclude that the conditional tail expectations of a wide range of loss distributions can be analytically obtained using the methods shown in this article.

Original languageEnglish
Pages (from-to)198-216
Number of pages19
JournalNorth American Actuarial Journal
Volume14
Issue number2
DOIs
Publication statusPublished - 2010 Apr 1

Fingerprint

Exponential Family
Tail
Moment
Generalized Hyperbolic Distribution
Natural Exponential Family
Canonical Representation
Risk Measures
Risk Management
Pareto
Finance
Insurance
Conditioning
Univariate
Explicit Formula
Exponential family
Conditional tail expectation
Range of data
Loss distribution

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

Cite this

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Conditional tail moments of the exponential family and its related distributions. / Kim, Joseph H.T.

In: North American Actuarial Journal, Vol. 14, No. 2, 01.04.2010, p. 198-216.

Research output: Contribution to journalArticle

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