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This article is cited in 9 scientific papers (total in 9 papers)
Short Communications
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.
DOI:
https://doi.org/10.4213/tvp335
 Full text:
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English version:
Theory of Probability and its Applications, 2001, 45:1, 136–147
Bibliographic databases:
  
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
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\jour Theory Probab. Appl.
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http://mi.mathnet.ru/eng/tvp335https://doi.org/10.4213/tvp335 http://mi.mathnet.ru/eng/tvp/v45/i1/p182
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This publication is cited in the following articles:
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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
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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
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L. M. Zaks, V. Yu. Korolev, “Obobschennye dispersionnye gamma-raspredeleniya kak predelnye dlya sluchainykh summ”, Inform. i ee primen., 7:1 (2013), 105–115
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V. Yu. Korolev, “Generalized hyperbolic laws as limit distributions for random sums”, Theory Probab. Appl., 58:1 (2014), 63–75
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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
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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
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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
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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
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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
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