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arXiv · 2004.10697

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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Abstract

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.

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Stefan Gerhold, Friedrich Hubalek, Richard B. Paris. 2020-04-22. The running maximum of the Cox-Ingersoll-Ross process with some properties of the Kummer function. https://arxiv.org/abs/2004.10697

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