확률지배이론으로 분석한 위험성의 증가와 최적손실통제
The Effects of Increases in Risk on Optimal Loss Control: A Stochastic Dominance Approach
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이 논문은 손실위험의 위험성의 증가가 최적손실통제에 주는 영향을 분석한다. 구체적으론, 주로 제1차 및 제2차 확률지배이론과 Kimball(1990)의 검약도(Degree of Prudence) 개념을 원용해, 손실위험의 위험성이 제1차 그리고 제2차의 확률지배의 형태를 따라 변화하는 경우 어떻게 최적손실통제의 행태가 바뀌는 가를 규명해 본다. 먼저 우리는 손실위험이 제1차 확률지배의 형태로 증가되는 경우, 일반적인 예상처럼, 리스크관리자가 손실통제에의 비용지출을 증가시키는데 요구되는 충분조건을 Arrow-Pratt의 절대 그리고 상대위험회피도를 이용한 효용함수에의 제약조건으로 도출했다. 하지만 손실위험이 제2차 확률지배의 형태로 변화되는 경우에는 더욱 복합적이고 제약적인 조건이 요구된다. 특히 이 경우 Arrow-Pratt의 위험회피도는 충분조건을 이끌어 내는 데 제 역할을 다하지 못한다. 우리는 Arrow-Pratt의 위험회피척도를 대신해 Kimball(1990)에 의해 개발된 절대검약(Absolute Prudence) 및 상대검약(Relative Prudence)의 척도를 이용해 비교적 간명한 충분조건을 유도해 낸다.
Abstract
We examine the effects of increases in risk on optimal loss control decision. We focus our attentions on the cases that the increases in risk take the form of both first degree and second degree stochastic dominance changes in risk. In particular, we derive a set of conditions, for each type of risk increases, that is sufficient for a risk averse decision maker to increase his investment level on loss control. For the case of risk change in type of first degree stochastic dominance the results of the comparative statics depend on Arrow-Pratt measures of risk aversion in a more or less complicated way. However in the case of risk change in type of second degree stochastic dominance Arrow-Pratt measures of risk aversion is no more useful tool to study the comparative statics. In essence, we obtain some meaningful comparative statics results by utilizing Kimball(1990)'s measures of Absolute and Relative Prudence.
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