Geodesic
Continuity theorems and algorithmical problems in classical risk model
Dalʹnevostočnyj matematičeskij žurnal, Tome 10 (2010) no. 2, pp. 153-161 
T. A. Kalmykova; Yu. N. Kharchenko; G. Sh. Tsitsiashvili. Continuity theorems and algorithmical problems in classical risk model. Dalʹnevostočnyj matematičeskij žurnal, Tome 10 (2010) no. 2, pp. 153-161. http://geodesic.mathdoc.fr/item/DVMG_2010_10_2_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper an analog of the Bernstein theorem about an approximation of a probability distribution by a mixture of exponential distribution is proved in the metric $L_1$. Different generalizations of classical risk model on a case of dependent financial and insurance risks are constructed. In this case a possibility of a paralleling of algorithms of ruin probability calculation is analyzed.

[1] G. Sh. Tsitsiashvili, “Vychislenie veroyatnosti razoreniya v klassicheskoi modeli riska”, Avtomatika i telemekhanika, 2009, no. 12, 187–194 | MR | Zbl

[2] R. Norberg, “Ruin problems with assets and liabilities of diffusion type”, Stochastic Process. Appl., 81:2 (1999), 255–269 | DOI | MR | Zbl

[3] Q. Tang, G. Tsitsiashvili, “Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks”, Stochast. Process. Appl., 108:2 (2003), 299–325 | DOI | MR | Zbl

[4] V. M. Zolotarev, “Stokhasticheskaya nepreryvnost sistem massovogo obsluzhivaniya”, Teoriya veroyatnostei i ee primeneniya, 21:2 (1976), 260–279 | MR | Zbl

[5] A. Feldmann, W. Whitt, “Fitting mixtures of exponentials to long-tailed distributions to analyze network perfomance models”, Perfomance Evaluation, 31 (1998), 245–279 | DOI | MR

[6] D. Dufresne, “Stochastic life annuities abstract”, American Actuarial Journal, 11:1 (2007), 136–157 | DOI | MR

[7] B. Ko, A. C. Y. Ng, “Stochastic Annuities”, Daniel Dufresne, Discussions of papers already published, American Actuarial Journal, 11:3 (2007), 170–171 | DOI | MR