보험계약자의 최적 손실포트폴리오 및 자산포트폴리오에 미치는 부의 효과
Wealth Effects on the Insured’s Optimal Loss Portfolio and Asset Portfolio
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Mossin(1968) 이래, DARA의 가정 하에서, 보험은 부(wealth)가 증가할수록 그 수요가 감소하는 열등재가 된다는 것은 잘 알려진 사실일 것이다. 우리의 논문은, Mossin(1968)의 결과를 근간으로 해, 추가적으로 부의 증감이 보험계약자가 선택하는 최적 손실포트폴리오 및 자산포트폴리오에 주는 영향을 조사해 본다. 우리의 연구 결과는 현대 경제학의 표준가설인 DARA의 경우 다음과 같이 요약된다. 부가 증가하면 DARA의 보험계약자는 열등재인 보험구매를 줄이게 된다(Mossin, 1968). 그 결과 보험료지출과 자기부담손해의 합계액인 손실포트폴리오는 분산위험은 물론 Rothschild·Stiglitz(1970)의 관점에서도 더욱 그 위험성이 높아지지만, 보험계약자가 궁극적으로 보유하게 되는 전체 기말 자산포트폴리오는 부가보험료의 절감으로 인해 그 기댓값 및 확실성등가(certainty equivalent)가 부의 증가보다도 빠른 속도로 향상된다. 아울러, 우리의 연구는 CARA 및 IARA에서의 결과물도 함께 제시한다.
Abstract
Since Mossin(1968), it has long been recognized that insurance is an inferior good within the decreasing absolute risk aversion. The purpose of this paper is to analyze, based on Mossin(1968), the wealth effects on insured’s optimal loss portfolio and asset portfolio, using a general expected utility maximization model. Our main results can be summarized as follows: In particular, if an utility function exhibits DARA, an increase in initial wealth reduces the optimal level of insurance and deteriorates the riskiness of loss portfolio, and so insured’s total risk-taking in the final asset portfolio would in fact increase. However, the certainty equivalent level as well as the mean value of asset portfolio is improved more than an increase in initial wealth due to the saving of insurance loading. The additional results for the case of CARA and IARA are also provided.
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