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.