Working Paper Article Version 1 This version is not peer-reviewed

A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and its Applications in Insurance and Finance

Version 1 : Received: 26 August 2019 / Approved: 28 August 2019 / Online: 28 August 2019 (04:00:41 CEST)

How to cite: Dassios, A.; Jang, J.; Zhao, H. A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and its Applications in Insurance and Finance. Preprints 2019, 2019080290 Dassios, A.; Jang, J.; Zhao, H. A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and its Applications in Insurance and Finance. Preprints 2019, 2019080290

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.

Subject Areas

contagion risk; insurance premium; aggregate claims; default-free bond pricing; self-exciting process; Hawkes process; CIR process

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