양측 모럴해저드와 상호 모니터링 하에서의 최적보험
The Optimal Insurance Contract under Double-Sided Moral Hazard and Cross Monitoring
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이 연구에서는 보험계약자와 보험회사가 손실규모와 손실원인에 관하여 서로 다른 사적 정보를 가지고 있는 상황에서의 최적보험계약 문제를 분석한다. 구체적으로는 계약자의 과실정도에 따라 보험금이 달라지는 계약을 상정하여, 계약자는 자신의 과실정도를 관찰할 수 있지만 보험자는 이를 관찰할 수 없고, 반면에 보험자는 손실규모를 관찰할 수 있지만 계약자는 그것을 관찰할 수 없는 상황에서의 최적계약 문제를 쌍방향 모니터링이 요구되는 양측 모럴해저드 모델을 이용하여 분석한다. 중요한 결과는 다음과 같이 요약된다. 첫째, 최적부보율은 보험자에 대한 보험계약자의 모니터링만이 허용되는 조건에서 가장 높고, 보험계약자에 대한 보험회사의 모니터링만이 허용되는 조건에서 가장 낮다. 둘째, 임의의 조건 하에서는 보험료 수준에 관계없이 최적부보율은 항상 1보다 작다. 셋째 보험자와 계약자가 동시에 서로에 대하여 모니터링을 하는 게임에서 적어도 하나의 내쉬균형이 존재한다.
Abstract
We consider the choice of the insurance coverage rate between an insurer and a policyholder: in a situation where the policyholder cannot observe the amount of damage, while the insurer cannot easily observe the degree of policyholder's fault. We analyze this problem using a double-sided moral hazard model, with two parties who mutually monitor each other. The main results of our research can be briefly described as follows: First, the optimal insurance coverage rate is highest when only the policyholder‘s monitoring is allowed, while the optimal insurance coverage rate is lowest when only the insurer monitors. Second, if some conditions related to the form of utility function are satisfied, the optimal insurance coverage is always partial insurance. This result is satisfied regardless of premium level. Third, in the game where two parties simultaneously choose between the two actions(monitoring and non-monitoring), there exists at least a Nash equilibrium.
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