Approximations of the tail probability of the product of dependent extremal random variables and applications

- The tail probability of products of dependent random variables.
- Extend the bivariate product to the multivariate case.
- Results for different max-domain of attractions.
- Ruin probabilities for a discrete-time insurance risk model as applications.

In this paper, we investigate the tail probability of the product X∏i=1nYi, where (X,Y1,…,Yn) follows a multivariate Sarmanov distribution. An explicit asymptotic formula is established for the tail probability of the product when X belongs to the Fréchet, Gumbel, or Weibull max-domain of attraction. As applications, we consider a discrete-time risk model with dependent insurance and financial risks, and obtain the asymptotic behavior for the (in)finite-time ruin probabilities.