Valuing Changes in Investment Opportunities

• 成果类型: Article
• 署名作者: Abbas, Ali E.
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.1120.1092
• 发表日期: 2012
• 页码: 1451-1460
• 关键词: risk-aversion

摘要

Arrow and Pratt introduced a measure of risk aversion the negative ratio of the second to the first derivative of the utility function. This measure has found widespread use in the valuation of uncertain lotteries and in the calculation of the risk premium of an investment. This paper introduces two new measures for characterizing changes in the valuation of uncertain lotteries when their outcomes are modified by a monotone transformation. The first is a characteristic transformation of a utility function, U. and a monotone transformation, g. The shape of the characteristic transformation determines an upper bound, lower bound, or equality on the magnitude of the certainty equivalent of the modified lottery. The second is a measure of change in certainty equivalent, eta(g), whose sign also determines upper or lower bounds, and whose magnitude determines the change in value of a small-risk lottery when its outcomes are modified by a monotone transformation. For shift (and scale) transformations on the lottery outcomes, both the characteristic transformation and the measure of change, eta(g), provide new characterizations for the notions of decreasing absolute (and relative) risk aversion with wealth. Subject classifications: utility theory; risk attitude; valuation. Area of review: Decision Analysis. History: Received January 2010; revisions received July 2010, January 2011, March 2011, September 2011, January 2012, March 2012; accepted June 2012. Published online in Articles in Advance November 20, 2012.