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Modelling and comparing dependencies in multivariable risk portfolios. (English) Zbl 1137.91484
Summary: In this paper we investigate multivariate risk portfolios, where the risks are dependent. By proving some natural models for risk portfolios with the same marginal distributions we are able to compare two portfolios with different dependence structure with respect to their stop-loss premiums. In particular, some comparison results for portfolios with two-point distributions are obtained The analysis is based on the concept of the so-called supermodular ordering. We also give some numerical results which indicate that dependencies in risk portfolios can have a severe impact on the stop-loss premium. In fact, we show that the effect of dependencies can grow beyond any given bound.

MSC:
 91B30 Risk theory, insurance (MSC2010) 91B28 Finance etc. (MSC2000) 62P05 Applications of statistics to actuarial sciences and financial mathematics
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References:
 [1] Probability Inequalities in multivariate Distributions (1980) · Zbl 0455.60003 [2] DOI: 10.1080/03610929308831203 · Zbl 0786.62019 [3] DOI: 10.1016/0047-259X(85)90088-0 · Zbl 0572.62041 [4] Effective Actuarial Methods 3 (1990) [5] An introduction to Probability Theory and Its Applications. Volume II (1966) [6] Insurance: Mathematics and Economics 19 pp 243– (1997) [7] DOI: 10.2143/AST.26.2.563219 [8] Probability Theory (1978) [9] DOI: 10.1017/S0269964800004769 · Zbl 1096.60518 [10] DOI: 10.2307/3215390 · Zbl 0885.60081 [11] DOI: 10.1080/15326349708807420 · Zbl 0871.60015 [12] DOI: 10.1016/0167-7152(86)90039-8 · Zbl 0587.60017 [13] DOI: 10.1006/jmva.1997.1656 · Zbl 0883.60016 [14] Stochastic Orders and their Applications (1994) · Zbl 0806.62009 [15] DOI: 10.1090/S0002-9939-1986-0835875-8 [16] Insurance: Mathematics and Economics 21 pp 219– (1997) [17] Insurance: Mathematics and Economics 17 pp 215– (1996) [18] Inequalities: Theory of Majorization and its Applications (1979) · Zbl 0437.26007 [19] DOI: 10.2307/3215055 · Zbl 0855.60017 [20] DOI: 10.1016/0167-7152(93)90211-Z · Zbl 0779.60012 [21] Insurance: Mathematics and Economics 5 pp 197– (1986) [22] DOI: 10.2307/1911158 · Zbl 0616.90005 [23] Preprint (1997) [24] DOI: 10.1214/aos/1176347026 · Zbl 0679.60025 [25] DOI: 10.1214/aop/1176994668 · Zbl 0459.62010
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