Geodesic
Nonparametric estimation of the ruin probability for generalized
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 1, pp. 3-20

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In this paper we construct a statistical estimator of the ruin probability for a generalized risk process characterized by the stochastic character of the premium rate and of the intensity of insurance payments. The asymptotic properties of the proposed estimator are considered. Algorithms are proposed for the construction of approximate nonparametric confidence intervals for the ruin probability.
Keywords: risk process, generalized risk process, ruin probability, random sequences with random indices, unbiasedness, consistency, confidence intervals. 
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     author = {V. E. Bening and V. Yu. Korolev},
     title = {Nonparametric estimation of the ruin probability for generalized},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {3--20},
     publisher = {mathdoc},
     volume = {47},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_1_a0/}
}
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V. E. Bening; V. Yu. Korolev. Nonparametric estimation of the ruin probability for generalized. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 1, pp. 3-20. http://geodesic.mathdoc.fr/item/TVP_2002_47_1_a0/