Geodesic
Bounds for a sum of random variables under a mixture of normals
Teoriâ slučajnyh processov, Tome 13 (2007) no. 4, pp. 82-97.

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In two papers: Dhaene et al. (2002). Insurance: Mathematics and Economics 31, pp.3-33 and pp. 133-161, the approximation for sums of random variables (rv’s) was derived for the case where the distribution of the components is lognormal and known, but the stochastic dependence structure is unknown or too cumbersome to work with. In finance and actuarial science a lot of attention is paid to a regime switching model. In this paper we give the approximation for sums under a mixture of normals and consider approximate evaluation of provision under switching regime.
Keywords: Convex stochastic order, bounds for provision, regime switching model. 
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Alexander Kukush; Mykhailo Pupashenko. Bounds for a sum of random variables under a mixture of normals. Teoriâ slučajnyh processov, Tome 13 (2007) no. 4, pp. 82-97. http://geodesic.mathdoc.fr/item/THSP_2007_13_4_a5/

[1] J. Dhaene, M. Denuit, M. J. Goovaerts, R. Kaas, D. Vyncke, “The concept of comonotonicity in actuarial science and finance: theory Insurance”, Mathematics and Economics, 31 (2002a), 3–33

[2] J. Dhaene, M. Denuit, M. J. Goovaerts, R. Kaas, D. Vyncke, “The concept of comonotonicity in actuarial science and finance: applica- tions Insurance”, Mathematics and Economics, 31 (2002b), 133–161

[3] H. Yang, “Optimal portfolio strategy under regime switching model”, Proceedings of the Twelfth International Conference on Computational and Applied Mathematics ICCAM 2006, Leuven, Belgium, 2006