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

Research output: Contribution to journal › Article › peer-review

5 Downloads (Pure)

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

Access to Document

10.54379/jiasf-2022-2-1

Paris_TheRunningMaximum_Published_2022Final published version, 407 KB

Cite this

@article{f43c5ea6e7814c1399523d90851bca5f,

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.",

author = "Stefan Gerhold and Friedrich Hubalek and Paris, {Richard B.}",

note = "Funding information: Stefan Gerhold was supported by the Austrian Science Fund (FWF) under grant P 30750.",

year = "2022",

month = jan,

day = "22",

doi = "10.54379/jiasf-2022-2-1",

language = "English",

volume = "13",

pages = "1--18",

journal = "Journal of Inequalities and Special Functions",

issn = "2217-4303",

number = "2",

}

TY - JOUR

T1 - The running maximum of the Cox-Ingersoll-Ross process with some properties of the Kummer function

AU - Gerhold, Stefan

AU - Hubalek, Friedrich

AU - Paris, Richard B.

N1 - Funding information: Stefan Gerhold was supported by the Austrian Science Fund (FWF) under grant P 30750.

PY - 2022/1/22

Y1 - 2022/1/22

N2 - 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.

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.

U2 - 10.54379/jiasf-2022-2-1

DO - 10.54379/jiasf-2022-2-1

M3 - Article

VL - 13

SP - 1

EP - 18

JO - Journal of Inequalities and Special Functions

JF - Journal of Inequalities and Special Functions

SN - 2217-4303

IS - 2

ER -

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

Abstract

Keywords

Access to Document

Fingerprint

Cite this