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

Stefan Gerhold; Friedrich Hubalek; Richard B. Paris

doi:10.54379/jiasf-2022-2-1

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 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 language	English
Pages (from-to)	1-18
Number of pages	18
Journal	Journal of Inequalities and Special Functions
Volume	13
Issue number	2
DOIs	https://doi.org/10.54379/jiasf-2022-2-1
Publication status	Published - 22 Jan 2022

Keywords

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

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10.54379/jiasf-2022-2-1

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title = "The running maximum of the Cox-Ingersoll-Ross process with some properties of the Kummer function",

abstract = "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.",

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AB - 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.

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DO - 10.54379/jiasf-2022-2-1

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

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