Title: Stochastic comparisons of the largest claim amounts from two sets of interdependent heterogeneous portfolios,
Abstract: Let $ X_{\lambda_1},\ldots,X_{\lambda_n}$ be dependent non-negative random
variables and $Y_i=I_{p_i} X_{\lambda_i}$, $i=1,\ldots,n$, where
$I_{p_1},\ldots,I_{p_n}$ are independent Bernoulli random variables independent
of $X_{\lambda_i}$'s, with ${\rm E}[I_{p_i}]=p_i$, $i=1,\ldots,n$. In actuarial
sciences, $Y_i$ corresponds to the claim amount in a portfolio of risks. In
this paper, we compare the largest claim amounts of two sets of interdependent
portfolios, in the sense of usual stochastic order, when the variables in one
set have the parameters $\lambda_1,\ldots,\lambda_n$ and $p_1,\ldots,p_n$ and
the variables in the other set have the parameters
$\lambda^{*}_1,\ldots,\lambda^{*}_n$ and $p^*_1,\ldots,p^*_n$. For
illustration, we apply the results to some important models in actuary.