Statistical premium in correlated losses of insurance

We first investigate the market under two losses in which the second loss was affected by the first loss. We calculate the associated statistical premium using global and independent methods. The results show that the premium calculated in the global method is larger than that calculated in the independent method. Next, we consider the markets with more general losses which are correlated to one another. We adopt the “principle of minimum sensitive dependence on risk aversion” to find the statistical premium with the help of the Lagrange multiplier method. It is shown that the statistical premium found by using this method is larger than that calculated by using the independent method. We also show that when there is larger uncertainty, there is larger need for a risk loading in global condition. When the risk aversion is introduced, all insured prefer to move from their originally optimal loss control activities to a combination of the lower dispersion and risk tolerance. This also corroborates that increasing in risk reduces the optimal risk exposure of the application and induce the insured's loss control mechanisms adopted on insurance pricing and premium adjustments.