# Risk Model Based on General Compound Hawkes Process

## TL;DR

This paper introduces a novel risk model using a general compound Hawkes process, establishing fundamental probabilistic results and analyzing key risk metrics, with applications to classical models.

## Contribution

It develops a new risk model based on the general compound Hawkes process and proves LLN and FCLT, extending classical risk models with new stochastic properties.

## Key findings

- Proved Law of Large Numbers for the model
- Established Functional Central Limit Theorem
- Derived properties like net profit condition and ruin time

## 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).