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Teor. Veroyatnost. i Primenen., 2000, Volume 45, Issue 1, Pages 182–194 (Mi tvp335)  

This article is cited in 9 scientific papers (total in 9 papers)

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Asymptotic properties of extrema of compound Cox processes and their applications to some problems of financial mathematics

V. Yu. Korolev

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: 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.


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English version:
Theory of Probability and its Applications, 2001, 45:1, 136–147

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Received: 11.02.1998

Citation: V. Yu. Korolev, “Asymptotic properties of extrema of compound Cox processes and their applications to some problems of financial mathematics”, Teor. Veroyatnost. i Primenen., 45:1 (2000), 182–194; Theory Probab. Appl., 45:1 (2001), 136–147

Citation in format AMSBIB
\by V.~Yu.~Korolev
\paper Asymptotic properties of extrema of compound Cox processes and their applications to some problems of financial mathematics
\jour Teor. Veroyatnost. i Primenen.
\yr 2000
\vol 45
\issue 1
\pages 182--194
\jour Theory Probab. Appl.
\yr 2001
\vol 45
\issue 1
\pages 136--147

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    This publication is cited in the following articles:
    1. Ng K.W., Tang Q.H., Yan J.A., Yang H.L., “Precise large deviations for sums of random variables with consistently varying tails”, Journal of Applied Probability, 41:1 (2004), 93–107  crossref  mathscinet  zmath  isi  scopus
    2. Tang Q.H., “Uniform estimates for the tail probability of maxima over finite horizons with subexponential tails”, Probability in the Engineering and Informational Sciences, 18:1 (2004), 71–86  crossref  mathscinet  zmath  isi  scopus
    3. L. M. Zaks, V. Yu. Korolev, “Obobschennye dispersionnye gamma-raspredeleniya kak predelnye dlya sluchainykh summ”, Inform. i ee primen., 7:1 (2013), 105–115  mathnet
    4. V. Yu. Korolev, “Generalized hyperbolic laws as limit distributions for random sums”, Theory Probab. Appl., 58:1 (2014), 63–75  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. V. Yu. Korolev, L. M. Zaks, A. I. Zeifman, “O skhodimosti sluchainykh bluzhdanii, porozhdennykh obobschennymi protsessami Koksa, k protsessam Levi”, Inform. i ee primen., 7:2 (2013), 84–91  mathnet
    6. Korolev V.Yu. Zaks L.M. Zeifman A.I., “On Convergence of Random Walks Generated by Compound Cox Processes to Levy Processes”, Stat. Probab. Lett., 83:10 (2013), 2432–2438  crossref  mathscinet  zmath  isi  elib  scopus
    7. M. E. Grigoreva, V. Yu. Korolev, “O skhodimosti raspredelenii sluchainykh summ k skoshennym eksponentsialno-stepennym zakonam”, Inform. i ee primen., 7:4 (2013), 66–74  mathnet  crossref  elib
    8. Korolev V.Yu. Chertok A.V. Korchagin A.Yu. Zeifman A.I., “Modeling High-Frequency Order Flow Imbalance By Functional Limit Theorems For Two-Sided Risk Processes”, Appl. Math. Comput., 253 (2015), 224–241  crossref  mathscinet  zmath  isi  scopus
    9. Korolev V.Yu. Zeifman A.I., “Convergence of Statistics Constructed From Samples With Random Sizes to the Linnik and Mittag-Leffler Distributions and Their Generalizations”, J. Korean Stat. Soc., 46:2 (2017), 161–181  crossref  mathscinet  zmath  isi  scopus
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