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.
| Original language | English |
|---|---|
| Article number | 103 |
| Pages (from-to) | 1-18 |
| Number of pages | 18 |
| Journal | Risks |
| Volume | 7 |
| Issue number | 4 |
| Early online date | 2019 |
| DOIs | |
| Publication status | Published - Dec 2019 |
Bibliographical note
Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.Keywords
- contagion risk
- insurance premium
- aggregate claims
- default-free bond pricing
- self-exciting process
- hawkes process
- CIR process
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