Geodesic
Ordering results for aggregate claim amounts from two heterogeneous Marshall--Olkin extended exponential portfolios and their applications in insurance analysis
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 1, pp. 145-162

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In this work, we discuss the stochastic comparison of two classical surplus processes in a one-year insurance period. Under the Marshall–Olkin extended exponential random aggregate claim amounts, we extend one result of Khaledi and Ahmadi [J. Statist. Plann. Inference, 138 (2008), pp. 2243–2251]. Applications of our results to the value-at-risk and ruin probability are also given. Our results show that the heterogeneity of the risks in a given insurance portfolio tends to make the portfolio volatile, which in turn leads to requiring more capital.
Keywords: Marshall–Olkin extended exponential distribution, usual multivariate stochastic order, multivariate chain majorization, order statistics, hazard rate function, aggregate claim amounts, value-at-risk, ruin probability. 
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G. Barmalzan; A. T. Payandeh Najafabadi; N. Balakrishnan. Ordering results for aggregate claim amounts from two heterogeneous Marshall--Olkin extended exponential portfolios and their applications in insurance analysis. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 1, pp. 145-162. http://geodesic.mathdoc.fr/item/TVP_2017_62_1_a8/