Risk vulnerability and the tempering effect of background risk
Risk vulnerability and the tempering effect of background risk
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DOI：
10.2307/2171958
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发表时间：
1996-09-01
期刊：
影响因子：
6.1
通讯作者：
Pratt, JW
中科院分区：
文献类型：
--
作者：
Gollier, C;Pratt, JW
我们在本文中研究了效用函数的一个新的自然限制，即在财富中加入不公平的背景风险，会使风险厌恶的个人在任何其他独立风险方面表现得更加厌恶风险。这个概念被称为风险脆弱性。它相当于一个条件，即一个不可取的风险永远不会因为一个独立的、不公平的风险的存在而变得可取。此外，在风险脆弱性下，增加一个不公平的背景风险降低了对风险资产的需求。风险脆弱性概括了Pratt和Zeckhauser（1987）提出的适当性概念（单独不受欢迎，独立风险总是共同不受欢迎）。这意味着效用函数的两个一阶导数是原始效用函数的凹变换。在绝对风险厌恶递减的情况下，风险脆弱性的一个充分条件是局部适当性，即r“r "r，其中r是绝对风险厌恶的Arrow-Pratt系数。
We examine in this paper a new natural restriction on utility functions, namely that adding an unfair background risk to wealth makes risk-averse individuals behave in a more risk-averse way with respect to any other independent risk. This concept is called risk vulnerability. It is equivalent to the condition that an undesirable risk can never be made desirable by the presence of an independent, unfair risk. Moreover, under risk vulnerability, adding an unfair background risk reduces the demand for risky assets. Risk vulnerability generalizes the concept of properness (individually undesirable, independent risks are always jointly undesirable) introduced by Pratt and Zeckhauser (1987). It implies that the two first derivatives of the utility function are concave transformations of the original utility function. Under decreasing absolute risk aversion, a sufficient condition for risk vulnerability is local properness, i.e. r '' r'r, where r is the Arrow-Pratt coefficient of absolute risk aversion.