Risk Model Based on General Compound Hawkes Process
Abstract
In this paper, we introduce a new model for the risk process based on general compound Hawkes process (GCHP) for the arrival of claims. We call it risk model based on general compound Hawkes process (RMGCHP). The Law of Large Numbers (LLN) and the Functional Central Limit Theorem (FCLT) are proved. We also study the main properties of this new risk model, net profit condition, premium principle and ruin time (including ultimate ruin time) applying the LLN and FCLT for the RMGCHP. We show, as applications of our results, similar results for risk model based on compound Hawkes process (RMCHP) and apply them to the classical risk model based on compound Poisson process (RMCPP).
Cite
@article{arxiv.1706.09038,
title = {Risk Model Based on General Compound Hawkes Process},
author = {Anatoliy Swishchuk},
journal= {arXiv preprint arXiv:1706.09038},
year = {2017}
}
Comments
16 pages; this paper will be presented at the 21st International Congress Insurance: Mathematics and Economics-IME 2017, TUW, Vienna