기대의존성과 다수위험하의 베르누이원칙
Expectation Dependence and the Bernoulli Principle Under Multiple Sources of Risk
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이 논문에서는, 보험위험과 통계학적 상호의존성이 있는 외생적 배경위험이 존재하는 경우, Wright(1987)에 의해 개발된 ‘기대의존성(Expectation Dependence)’의 개념을 적용해 베르누이원칙이 성립할 수 있는 필요⋅충분조건을 유도하고, 또 확률분포의 예시를 통해 그 결과를 확인해 본다. 요컨대 보험위험과 배경위험 간에 양(+)의, ‘0’의, 또는 음(-)의 기대의존성이 있는 경우 보험계약자는 그 경우에 한해서만 일부보험, 전부보험, 또는 초과보험을 각각 구입한다. 이 논문의 연구결과는 베르누이원칙에 대해 단순한 충분조건들을 제시하고 있던 기존의 연구결과(Aboudi⋅Thon 1995, 홍순구 2001⋅2004)들을 크게 개선시킨다. 즉 기대의존성의 개념을 적용해 베르누이원칙에 요구되는 필요⋅충분조건의 범위를 규정한 것이다. 이 기대의존성은 Aboudi⋅Thon(1995)에서의 회귀의존성이나 홍순구(2001, 2004)에서의 상호의존성을 포함하는 보다 광범위한 상호의존성의 개념이 된다.
Abstract
This paper examines the Bernoulli Principle when an individual faces both a background risk and an interdependent insurable risk. The background risk is modelled as an initial random wealth. Within this model, using "expectation dependence" developed by Wright(1987), we provide the necessary and sufficient conditions for the Bernoulli Principle to hold or violate. That is, it is shown that the rational individual would buy less than, full or more than full insurance if and only if the expectation dependence is positive, zero or negative, respectively. These results extend the recent conclusion of, for example, Aboudi.Thon(1995) or Hong(2001, 2004) in two ways: 1.The notions of expectation dependence are less restrictive than those of regression dependence in Aboudi.Thon(1995) or those of Brumelle(1974)'s interdependence in Hong(2001, 2004); 2.We give conditions that are both necessary and sufficient, while Aboudi.Thon(1995) or Hong(2001, 2004) suggested only the sufficient, but not necessary, conditions for the Bernoulli Principle.
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