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

2018/12/14 by Hossein Nadeb, Nadeb, Hossein, Hamzeh Torabi +3
Decision Sciences · Economics, Econometrics and Finance · #FOS: Economics and business #FOS: Mathematics #Insurance and Financial Risk Management #Probability and Risk Models #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1812.08343

openalex publication_date 2018/12/14 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28

Abstract

Let X_\λ1,\…,X_\λn be dependent non-negative random\nvariables and Y_i=I_pi X_\λi, i=1,\…,n, where\nI_p1,\…,I_pn are independent Bernoulli random variables independent\nof X_\λi's, with rm E[I_pi]=p_i, i=1,\…,n. In actuarial\nsciences, Y_i corresponds to the claim amount in a portfolio of risks. In\nthis paper, we compare the largest claim amounts of two sets of interdependent\nportfolios, in the sense of usual stochastic order, when the variables in one\nset have the parameters \λ₁,\…,\λ_n and p₁,\…,p_n and\nthe variables in the other set have the parameters\n\λ^*₁,\…,\λ^*_n and p^*₁,\…,p^*_n. For\nillustration, we apply the results to some important models in actuary.\n

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