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 |
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Pages (from-to) | 1-18 |
Number of pages | 18 |
Journal | Journal of Inequalities and Special Functions |
Volume | 13 |
Issue number | 2 |
DOIs | |
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