A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance
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 lit...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-10-01
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| Series: | Risks |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-9091/7/4/103 |
| _version_ | 1819071520691978240 |
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| author | Angelos Dassios Jiwook Jang Hongbiao Zhao |
| author_facet | Angelos Dassios Jiwook Jang Hongbiao Zhao |
| author_sort | Angelos Dassios |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-21T17:23:08Z |
| format | Article |
| id | doaj.art-f6c229aa628740838bd2dd8048f2258e |
| institution | Directory Open Access Journal |
| issn | 2227-9091 |
| language | English |
| last_indexed | 2024-12-21T17:23:08Z |
| publishDate | 2019-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Risks |
| spelling | doaj.art-f6c229aa628740838bd2dd8048f2258e2022-12-21T18:56:07ZengMDPI AGRisks2227-90912019-10-017410310.3390/risks7040103risks7040103A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and FinanceAngelos Dassios0Jiwook Jang1Hongbiao Zhao2Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, UKDepartment of Actuarial Studies & Business Analytics, Macquarie Business School, Macquarie University, Sydney NSW 2109, AustraliaSchool of Statistics and Management, Shanghai University of Finance and Economics, No. 777 Guoding Road, Shanghai 200433, ChinaIn 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.https://www.mdpi.com/2227-9091/7/4/103contagion riskinsurance premiumaggregate claimsdefault-free bond pricingself-exciting processhawkes processcir process |
| spellingShingle | Angelos Dassios Jiwook Jang Hongbiao Zhao A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance Risks contagion risk insurance premium aggregate claims default-free bond pricing self-exciting process hawkes process cir process |
| title | A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance |
| title_full | A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance |
| title_fullStr | A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance |
| title_full_unstemmed | A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance |
| title_short | A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance |
| title_sort | generalised cir process with externally exciting and self exciting jumps and its applications in insurance and finance |
| topic | contagion risk insurance premium aggregate claims default-free bond pricing self-exciting process hawkes process cir process |
| url | https://www.mdpi.com/2227-9091/7/4/103 |
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