Pareto-Optimal Insurance Policies in the Models with a Premium Based on the Actuarial Value

This article analyzes the problem of designing Pareto-optimal insurance policies when both the insurer and the insured are risk averse and the premium is calculated as a function of the actuarial value of the insurer's risk. Two models are considered: in the first, the set of admissible policies is constrained by a given size of the premium; in the second, the premium size is not constrained so that it varies with the actuarial value of a policy chosen by the agents. For both cases a characterization of the Pareto-optimal policies is derived. The corresponding optimality equations for the Pareto-optimal policies are obtained and compared with the results on the classical risk exchange model. Copyright The Journal of Risk and Insurance, 2006.