Correlated Risk Model Based on Compound Poisson Claim Count Process with Reinsurance and Investment

In this paper, we introduce a correlated aggregate claims risk model based on a compound Poisson counting process for non-equidispersed claim count data, incorporating with investment and reinsurance. Accordingly, the risk model has three distinct components: (1) the correlated risk model, which has multiple classes of insurance business where claims can be made from any type of various events, (2) the reinsurance strategy which is a combination of the excess of loss and quota-share reinsurance, which defends the insurer from risk exposure that results in large losses, (3) the investment, which strengthens the insurance company’s financial stability as a result of the relationship between return and volatility. The advancement of the proposed model is to accommodate non-equidispersed data commonly encountered in claim count data. Particularly, the proposed model covers two widely applied claim count processes, specifically the compound Poisson-binomial process and the compound Poisson-negative binomial process. In our study, we derive the model properties, obtain the optimal investment and reinsurance that maximize the adjustment coefficient and obtain the minimized upper bound of the ruin probability. Moreover, we perform numerical experiments to evaluate the performance of the proposed model based on the two claim count processes. In each scenario, we study impacts of reinsurance and investment to the upper bound of the ruin probability and obtain the optimal investment strategy.