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

2020/04/22 by Stefan Gerhold, Gerhold, Stefan, Friedrich Hubalek +3
Economics, Econometrics and Finance · Mathematics · #33C15 #41A60 #60G17 #Classical Analysis and ODEs (math.CA) #Economic theories and models #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2004.10697

openalex publication_date 2020/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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