단조우도비율(MLR)의 위험증가와 최적손실통제
Monotone Likelihood Ratio Increase in Risk and Optimal Loss Control
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초록
재무경제학에서 단조우도비율()의 확률체계는 지금까지도 여러 핵심적인 역할들을 수행해 오고 있지만, 보험관련문헌에선 거의 주목을 받지 못하고 있다. 본 연구는 이런 간격을 줄이고자 수행된다. 이 연구는 그 주된 목적으로 손실위험의 위험증가가 최적손실통제비용에 미치는 영향을 조사한다. 우리는 손실위험이 위험증가를 하는 경우, 증가하는 효용함수를 가진 모든 리스크관리자는, 그 위험성향에 관계없이, 손실통제비용을 일률적으로 증가시킨다는 결과를 입증한다. 의 이 연구결과는 손실위험이 임의의 1차확률지배() 형태로 위험증가하는 경우와도 비교⋅분석된다. 즉, 위험증가에선, 합리적 효용함수로 간주되는 일정절대위험회피() 및 감소절대위험회피()의 경우 일반적으로 그 충분조건을 만족시키지 못한다. 또한 본 연구에선, 보다 직관적으로, 위험증가는 확실성의 모형에서 손실액이 단순증가하는 경우와 동일한 최적손실통제의 행태를 유도하는 위험증가의 내용이 된다는 사실도 확인한다.
Abstract
Even though the monotone likelihood ratio (MLR) stochastic order has played crucial roles in the financial economics, it has received little attention in insurance literature. This article may shorten this gap. In essence, the main purpose of this paper is to investigate the comparative static problem: How do MLR increases in risk affect the optimal decision of loss control? We demonstrate that all risk managers with increasing utility function, without any restrictions on risk preferences, will increase optimal expenditure for loss control, in the presence of MLR increases in risk. We contrast this MLR result with that of the first-order stochastic dominance (FSD) increase in risk. In particular, it is shown that the sufficient conditions for arbitrary FSD increase in risk are so demanding that they rule out many reasonable utility functions such as constant absolute risk aversion (CARA) or decreasing absolute risk aversion (DARA). We also note an intuitive result that an MLR increase in risk is behaviorally identical to an increase in determinate loss under certainty model.
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