Risk measurement for insurance sector with credible tail value-at-risk

Providing protection against probability of losses is important issue in insurance company. Insurance company must certainly estimate all the risks which can be done by using risk measures. Value-at-Risk (VaR) is one of risk measures that is widely used in insurance industry. However, this risk measure can be inaccurate if there are loss values which far exceed the VaR value. In this paper, Tail Value-at-Risk (TVaR) can be more representative to be the risk measure. In practical uses, TVaR can represent the amount of capital that will be needed due to certain losses which possibly happen. Better risk estimation can also be obtained by combining both individual and group of policyholders risk. One method to combine both these risks is by using credibility theory which will give certain weights for both individual and group risk measures. The proper weights are obtained by minimizing the mean squared error between a parameter used to predict future losses and its estimator. In general, this paper will derive credible TVaR model which uses Bühlmann credibility theory. Individual risk will be represented by TVaR of certain policyholder; meanwhile, group of policyholders risk will be represented by the average of every policyholder's TVaR value. Estimator of each parameter used in the model will be derived as it will use real data for application. In the end of this paper, numerical simulation which uses one of Indonesia life insurance company's data about policyholder claims in certain periods of time will also be presented.