A Generalised CIR process with externally-exciting and self-exciting jumps and its applications in insurance and finance

Angelos Dassios, Jiwook Jang, Hongbiao Zhao

Research output: Contribution to journalArticle

2 Citations (Scopus)
1 Downloads (Pure)

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 languageEnglish
Article number103
Pages (from-to)1-18
Number of pages18
JournalRisks
Volume7
Issue number4
Early online date2019
DOIs
Publication statusPublished - 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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