A compound renewal model for medical malpractice insurance

A renewal model for the aggregate discounted payments and expenses assumed by the insurer is proposed for the “medical malpractice” insurance, where real interest rates could be stochastic and the dependencies between the expenses, the payments and the delays of payment are examined through the theory of copulas. As a first approach to this problem, we present formulas for the first two raw moments and the first joint moment of this aggregate risk process. Examples are given for Erlang claims interoccurence times and delays of payment, Pareto payments and expenses, and the influence of the dependency is illustrated by the Joe copula. Finally the distribution, VaR and TVaR of our risk process are also considered through simulations.