Convex Ordering of Random Variables and its Applications in Econometrics and Actuarial Science

Arjun K. Gupta, Mohammad A.S. Aziz

Abstract

It is well known that in economics and finance, the data usually have “fat tail” and in this case the Normal distribution is not a good model to use. The skew normal distributions recently draw considerable attention as an alternative model. Unfortunately, the distribution of the sum of log-skew normal random variables does not have a closed form. In this work, we discuss the use of lower convex order of random variables to approximate this distribution. Further, two application of this approximate distribution are given : first to describe the final wealth of a series of payments, and second to describe the present value of a series of payments.

Keywords

Log-skew normal random variable, Lower convex order bound, Comonotonocity

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