The expectation and variance of dependent random sums using copulas.

Random sums play an important role in insurance claim theory and risk models. This paper aims to explore the numerical characteristics of dependent random sums using copulas. We obtain theoretical formulae for the expectation and variance of random sums in the case of a general copula. The expectation is an extension of the Wald equality and can be used to estimate prospective value, while variance provides a theoretical guarantee for measuring the risk premium. As corollaries, the corresponding results for the compound Poisson process and random sums using Farlie-Gumbel-Morgenstern copulas have been obtained. We also conduct stochastic simulation to verify the accuracy of our theoretical results. [ABSTRACT FROM AUTHOR]