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Article

A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance

by
Angelos Dassios
1,*,
Jiwook Jang
2 and
Hongbiao Zhao
3
1
Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, UK
2
Department of Actuarial Studies & Business Analytics, Macquarie Business School, Macquarie University, Sydney NSW 2109, Australia
3
School of Statistics and Management, Shanghai University of Finance and Economics, No. 777 Guoding Road, Shanghai 200433, China
*
Author to whom correspondence should be addressed.
Risks 2019, 7(4), 103; https://doi.org/10.3390/risks7040103
Submission received: 26 August 2019 / Revised: 8 October 2019 / Accepted: 10 October 2019 / Published: 14 October 2019
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Abstract

In this paper, we study a generalised CIR process with externally-exciting and self-exciting jumps, and focus on the distributional properties and applications of this process and its aggregated process. The aim of the paper is to introduce a more general process that includes many models in the literature with self-exciting and external-exciting jumps. The first and second moments of this jump-diffusion process are used to calculate the insurance premium based on mean-variance principle. The Laplace transform of aggregated process is derived, and this leads to an application for pricing default-free bonds which could capture the impacts of both exogenous and endogenous shocks. Illustrative numerical examples and comparisons with other models are also provided.
Keywords: contagion risk; insurance premium; aggregate claims; default-free bond pricing; self-exciting process; hawkes process; CIR process contagion risk; insurance premium; aggregate claims; default-free bond pricing; self-exciting process; hawkes process; CIR process

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MDPI and ACS Style

Dassios, A.; Jang, J.; Zhao, H. A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance. Risks 2019, 7, 103. https://doi.org/10.3390/risks7040103

AMA Style

Dassios A, Jang J, Zhao H. A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance. Risks. 2019; 7(4):103. https://doi.org/10.3390/risks7040103

Chicago/Turabian Style

Dassios, Angelos, Jiwook Jang, and Hongbiao Zhao. 2019. "A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance" Risks 7, no. 4: 103. https://doi.org/10.3390/risks7040103

APA Style

Dassios, A., Jang, J., & Zhao, H. (2019). A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance. Risks, 7(4), 103. https://doi.org/10.3390/risks7040103

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