Stochastic comparisons of the largest claim amounts from two sets of interdependent heterogeneous portfolios

12/14/2018

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by   Hossein Nadeb, et al.

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Let X_λ_1,...,X_λ_n be dependent non-negative random variables and Y_i=I_p_i X_λ_i, i=1,...,n, where I_p_1,...,I_p_n are independent Bernoulli random variables independent of X_λ_i's, with E[I_p_i]=p_i, i=1,...,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 λ_1,...,λ_n and p_1,...,p_n and the variables in the other set have the parameters λ^*_1,...,λ^*_n and p^*_1,...,p^*_n. For illustration, we apply the results to some important models in actuary.