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Ordering results for aggregate claim amounts from two heterogeneous Marshall-Olkin extended exponential portfolios and their applications in insurance analysis. (English) Zbl 1458.62232

Theory Probab. Appl. 62, No. 1, 117-131 (2018) and Teor. Veroyatn. Primen. 62, No. 1, 145-162 (2017).
Summary: 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 B.-E. Khaledi and S. S. Ahmadi [J. Stat. Plann. Inference 138, No. 7, 2243–2251 (2008; Zbl 1134.62071)]. 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.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
60E15 Inequalities; stochastic orderings
91G70 Statistical methods; risk measures

Citations:

Zbl 1134.62071
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References:

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