Ismail, Muhammad Iqbal Al-Banna (2023) Mathematical modeling of collective value at risk (CVAR) and collective modified value at risk (CMVAR) in life insurance collection for some compound distribution. Doctoral thesis, Universiti Tun Hussein Onn Malaysia.

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Abstract

It is known that life insurance claims involve large sums of money, so it is very important for the actuarial company of the insurance company to make risk analysis of the claim. In general, the risks associated with life insurance claims are measured using standard deviation and variance. However, standard deviation and variance could not accommodate all claim of risk occurrence. Thus, the question remains at how the standard deviation or variance to calculate individual risk parameters and collective risk in life insurance for some models related to the distribution of claims numbers and claim amount should be used. In this study, two models called Collective Value at Risk (CVaR) and Collective Modified Value at Risk (CMVaR) model were developed as two modification models to measure value on collective risk or risk. The main objective of this research is to achieve two models of collective value. In this collective risk model, the proposed method was performed for two models of distribution of claim number and claim amount. The collective results from the development of the Modified Value at Risk model are expected to meet each claim for risk events when given a certain level of significance. Data provided by Bank Negara Malaysia (BNM) have been used to identify the use and effectiveness of the CVaR model and CMVaR in this study. In the implementation of the CVaR model and the CMVaR models, the actual data from BNM was transformed by using Minitab 16 software. The next analysis is to use Microsoft Excel to build graphs, histograms and analysed the model being developed. In this analysis, the significance level chosen is from α = 0.5% to α = 4.0% for the two models being developed. Results show that both proposed method CVaR and CMVaR models acquired the required scores on Collective Risk. This indicates that the advantages were proven by comparing Collective Risk with CVaR and CMVaR, thus the objectives of this study have been achieved. In addition, results indicate that CMVaR has higher risk than CVaR

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