Sample dependence of risk premiums

An important problem in the banking and insurance industries is that of pricing risk. The two come together when a bank buys insurance to decrease the impact of potential operational risk losses. The price of such insurance hinges on the computation of risk premiums, which involves the computation of expected values with respect to the loss distribution. When the empirical data set is not large and loss distributions are inferred from the data, a large sample dependence of the premiums on the data is to be expected. The maximum entropy-based methodologies offer model-free, non- parametric procedures to determine probability densities from empirical data with high precision. At the same time, they provide us with a framework within which to study how the sample dependence is transferred from the data to the premiums via the density. It is the aim of our paper to show how this can be done.