Self-exciting jump processes and their asymptotic behaviour

Kristina Rognlien Dahl; Heidar Eyjolfsson

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arXiv · 2006.16663

Self-exciting jump processes and their asymptotic behaviour

Kristina Rognlien Dahl·Heidar Eyjolfsson

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Abstract

The purpose of this paper is to investigate properties of self-exciting jump processes. We derive the Laplace transform of SDE driven self-exciting processes with independent, identically distributed jump sizes. By using this Laplace transform, we find a recursive formula for the moments of the self-exciting process. The formula for the moments allow us to derive expressions for the expectation and variance of the self-exciting process. We show that self-exciting processes can exhibit both finite and infinite activity behaviour. Furthermore, we show that the scaling limit of the intensity process equals the strong solution of the square-root diffusion process(Cox-Ingersoll-Ross process) in distribution. As a particular example, we study the case of a linear intensity process and derive explicit expressions for the expectation and variance in this case.

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BibTeX RIS

Kristina Rognlien Dahl, Heidar Eyjolfsson. 2020-06-30. Self-exciting jump processes and their asymptotic behaviour. https://arxiv.org/abs/2006.16663

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