Limit Theorems for a Cox-Ingersoll-Ross Process with Hawkes Jumps
Author:
- Lingjiong ZhuLZLingjiong Zhu
- 1 September 2014
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 51 (3) , 699-712
Abstract
In this paper we propose a stochastic process, which is a Cox-Ingersoll-Ross process with Hawkes jumps. It can be seen as a generalization of the classical Cox-Ingersoll-Ross process and the classical Hawkes process with exponential exciting function. Our model is a special case of the affine point processes. We obtain Laplace transforms and limit theorems, including the law of large numbers, central limit theorems, and large deviations.Keywords
All Related Versions
This publication has 19 references indexed in Scilit:
- Process-level large deviations for nonlinear Hawkes point processesAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, 2014
- Ruin probabilities for risk processes with non-stationary arrivals and subexponential claimsInsurance: Mathematics and Economics, 2013
- Modelling microstructure noise with mutually exciting point processesQuantitative Finance, 2012
- Risk Processes with Non-stationary Hawkes Claims ArrivalsMethodology and Computing in Applied Probability, 2008
- Credit risk modeling with affine processesJournal of Banking & Finance, 2005
- Stochastic mortality in life insurance: market reserves and mortality-linked insurance contractsInsurance: Mathematics and Economics, 2004
- Large Deviations Techniques and Applications1998
- A Theory of the Term Structure of Interest RatesEconometrica, 1985
- Spectra of some self-exciting and mutually exciting point processesBiometrika, 1971
- Two Singular Diffusion ProblemsAnnals of Mathematics, 1951