Bootstrap control charts in monitoring value at risk in insurance

• Sample size for estimating VaR can vary, as it depends on the number of claims.
• An efficient monitoring scheme is proposed to quickly detect drifts in the VaR.
• A probabilistic control chart and the parametric bootstrap method are employed.
• The method is ready applicable in practice, a real example is presented.
• The proposed method helps to control risk measurement in insurance companies.

A risk measure is a mapping from the random variables representing the risks to a number. It is estimated using historical data and utilized in making decisions such as allocating capital to each business line or deposit insurance pricing. Once a risk measure is obtained, an efficient monitoring system is required to quickly detect any drifts in the risk measure. This paper investigates the problem of detecting a shift in value at risk as the most widely used risk measure in insurance companies. The probabilistic C control chart and the parametric bootstrap method are employed to establish a risk monitoring scheme in insurance companies. Since the number of claims in a period is a random variable, the proposed method is a variable sample size scheme. Monte Carlo simulations for Weibull, Burr XII, Birnbaum–Saunders and Pareto distributions are carried out to investigate the behavior and performance of the proposed scheme. In addition, a real example from an insurance company is presented to demonstrate the applicability of the proposed method.