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Erscheinungsjahr: 
2019
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[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 7 [Issue:] 4 [Article No.:] 103 [Publisher:] MDPI [Place:] Basel [Year:] 2019 [Pages:] 1-18
Verlag: 
MDPI, Basel
Zusammenfassung: 
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.
Schlagwörter: 
aggregate claims
CIR process
contagion risk
default-free bond pricing
hawkes process
insurance premium
self-exciting process
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