Gerhold, S., Hubalek, F., & Paris, R. B. (2022). The running maximum of the Cox-Ingersoll-Ross process with some properties of the Kummer function. Journal of Inequalities and Special Functions, 13(2), 1–18. https://doi.org/10.54379/jiasf-2022-2-1
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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Mathematical Methods in Economics: 5% Fundamental Mathematics Research: 95%
