Dassios, A.; Jang, J.; Zhao, H. A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance. Risks2019, 7, 103.
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.
Dassios, A.; Jang, J.; Zhao, H. A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance. Risks2019, 7, 103.
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.
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 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 the 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
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
