IJPAM: Volume 44, No. 3 (2008)


Werner Hürlimann
IRIS Integrated Risk Management AG
Bederstrasse 1, Zürich, CH-8027, SWITZERLAND
e-mail: werner.huerlimann@irisunified.com
url-s: www.irisunified.com, www.geocities.com/hurlimann53

Abstract.The state of a Brownian motion after an exponentially distributed random time with normally distributed initial state generates a four-parameter Gaussian type distribution, called Normal-Laplace distribution, which exhibits two-sided fatter than normal tail behavior. Limiting cases include three-parameter Normal-Exponential distributions, which exhibit fatter than normal tail behavior in either the right-tail or the left-tail of the distribution. The application of these Gaussian type distributions to the analytical approximation of aggregate claims distributions is compared to earlier good approximations based on the translated gamma distribution, translated inverse Gaussian distribution and a mixture thereof. Quantitative improvement on the latter approximations is shown through numerical illustration.

Received: January 31, 2008

AMS Subject Classification: 62P05, 91B30

Key Words and Phrases: Brownian motion, Normal-Laplace, Normal-Exponential, gamma, translated gamma, translated inverse Gaussian, mixtures, aggregate claims

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 44
Issue: 3