Applications of IHREs in Insurance: Risk Model Based on General Compound Hawkes Process

This chapter introduces a new model for the risk process based on general compound Hawkes process for the arrival of claims, which is called as risk model based on general compound Hawkes process (RMGCHP). It proves the law of large lumbers (LLN) and the functional central limit theorem (FCLT). The chapter obtains LLN and FCLT for RMGCHP using martingale methods and change of time method. It contains applications of LLN and FCLT, including net profit condition, premium principle, ruin and ultimate ruin probabilities, and the probability density function of the time to ruin for RMGCHP. The chapter also discusses the applications of LLN and FCLT to the classical risk model based on compound Poisson process.