Hawkes processes in insurance: Risk model, application to empirical data and optimal investment

Anatoliy Swishchuk, Rudi Zagst and Gabriela Zeller

Insurance: Mathematics and Economics, 2021, vol. 101, issue PA, 107-124

Abstract: In this paper we study a risk model with claim arrivals based on general compound Hawkes processes and show that it is suitable to model empirical insurance data. We review a law of large numbers and functional central limit theorem for this model and derive a pure diffusion approximation which allows analytical calculation of finite-time and infinite-time ruin probabilities. We use the approximation to study the influence of replacing the classical Poisson arrival process by a general compound Hawkes process on optimal investment strategies for an insurer in an incomplete market by applying results from asset–liability management.

Keywords: Hawkes process; General compound Hawkes process; Risk model; FCLT; Diffusion approximation; Optimal investment for insurers; Incomplete market (search for similar items in EconPapers)
JEL-codes: G22 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:101:y:2021:i:pa:p:107-124

DOI: 10.1016/j.insmatheco.2020.12.005

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