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

We derive tail asymptotics for the running maximum of the Cox-Ingersoll-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.

preprint2020arXivOpen access
Stefan GerholdFriedrich HubalekRichard B. Paris
math.PRmath.CA
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Stefan GerholdFriedrich HubalekRichard B. Paris

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