Geodesic
Asymptotic properties of extrema of compound Cox processes and their applications to some problems of financial mathematics
Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 1, pp. 182-194

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Necessary and sufficient conditions are presented for the weak convergence of one-dimensional distributions of extrema of compound doubly stochastic Poisson processes whose jumps have zero expectation and finite variance. Convergence rate estimates are given. The obtained results are applied to the problem of prediction of stock prices.
Keywords: doubly stochastic Poisson process (Cox process), compound Cox process, maximum sums of independent random variables. 
@article{TVP_2000_45_1_a11,
     author = {V. Yu. Korolev},
     title = {Asymptotic properties of extrema of compound {Cox} processes and their applications to some problems of financial mathematics},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {182--194},
     publisher = {mathdoc},
     volume = {45},
     number = {1},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2000_45_1_a11/}
}
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V. Yu. Korolev. Asymptotic properties of extrema of compound Cox processes and their applications to some problems of financial mathematics. Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 1, pp. 182-194. http://geodesic.mathdoc.fr/item/TVP_2000_45_1_a11/