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Article
A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and its Applications in Insurance and Finance
This version is not peer-reviewed.
Submitted:
26 August 2019
Posted:
28 August 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 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
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
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