Investigating the collective value at risk model (CVaR) and its application on real data for life insurance

Life insurance is designed to reduce the risk of financial loss due to unforeseen consequences related to the insured's death. In life insurance, the insurer provides death benefits as a claim when the insured suffers death. The claim is the compensation for a risk loss. Individual claim in one-period insurance is called aggregation claim, while aggregation claim is a collective risk. Collective risk is usually measured using a variance. However, the variance risk measure cannot often accommodate any event risk because there is a risk of claims beyond the amount of variance. Using the proposed method CVaR and confidence level are taken from α = 0.25% until 4%. This study found that the proposed method CVaR scored more fairly than Collective Risk. In conclusion, this study indicated that the collective risk model is just included using mean and variance without any confidence level. Therefore, only one result for the Collective Risk model, which automatically shows the model using mean, variance and standard deviation, could not accommodate all risk events.