The running maximum of the Cox-Ingersoll-Ross process with some properties of the Kummer function

Stefan Gerhold, Friedrich Hubalek, Richard B. Paris

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    We derive tail asymptotics for the running maximum of the CoxIngersoll-Ross process. The main result is proved by the saddle point method, where the tail estimate uses a new monotonicity property of the Kummer function. This auxiliary result is established by a computer algebra assisted proof. Moreover, we analyse the coefficients of the eigenfunction expansion of the running maximum distribution asymptotically.
    Original languageEnglish
    Pages (from-to)1-18
    Number of pages18
    JournalJournal of Inequalities and Special Functions
    Issue number2
    Publication statusPublished - 22 Jan 2022


    • Kummer function
    • Confluent hypergeometric function
    • Cox-Ingersoll-Ross process
    • Running maximum
    • Saddle point method
    • Computer algebra
    • Eigenfunction expansion

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