IJPAM: Volume 108, No. 1 (2016)

ON THE TAIL BEHAVIOR OF
FUNCTIONS OF RANDOM VARIABLES

A.N. Kumar$^1$, N.S. Upadhye$^2$
$^{1,2}$Department of Mathematics
Indian Institute of Technology Madras
Chennai, 600036, INDIA


Abstract. It is shown that the tail behavior of the function of nonnegative random variables can be characterized using deterministic functions satisfying certain properties. Also, the upper and lower bounds for the tail of product of random variables are given. Applications of these results are given to some of the well-known models in economics and risk theory.

Received: January 21, 2016

AMS Subject Classification: 60E05, 60E15, 62P20, 91B30, 91B40

Key Words and Phrases: Natural scale function, Tail behavior, Ruin probability

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DOI: 10.12732/ijpam.v108i1.12 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 1
Pages: 123 - 139


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