A note on the satisfaction levels of two agents subscribing an insurance policy

Insurance Markets and Companies: Analyses and Actuarial Computations, Volume 4, Issue 2, 2013 Maria Erminia Marina (Italy), Marina Ravera (Italy) A note on the satisfaction levels of two agents subscribing an insurance policy Abstract Classical actuarial theory focuses on insurance problems and in particular on the determination of a premium for the insured risk. However, once a premium has been chosen, at the end of the insurance period it may happen that the policy has been disadvantageous either for the insurer or for the customer. In fact, the premium was not set high enough to cover the total claim amount or, vice versa, it was too high from the customer point of view. Our aim is to introduce, for each agent, a measurement in order to value how he is restrained in his possibilities. More precisely, the authors define two “satisfaction levels” that compare the increment in the expected utility that each agent has subscribing the insurance policy, with the increment in the expected utility that he could have if, unrealistically speaking, the insurer (customer) could withdraw from the contract in the case where the total claim amount is larger (smaller) than the premium, so that he never could have losses. Under assumptions, the authors show that the satisfaction levels are linked to the risk aversion of the agents, proving that inequalities comparing risk aversion of two insurers (customers) are related to inequalities between their satisfaction levels. Finally, the determination of a “fair” premium for an insurance contract is considered.