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Pessimistic Portfolio Choice with One Safe and One Risky Asset and Right Monotone Probability Difference Order

机译：具有一种安全和一种风险资产以及正确的单调概率差阶的悲观投资组合选择

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摘要

As is well known, a first-order dominant deterioration in risk does not necessarily cause a risk-averse investor to reduce his holdings of that deteriorated asset under the expected utility framework, even in the simplest portfolio setting with one safe asset and one risky asset. The purpose of this paper is to derive conditions on shifts in the distribution of the risky asset under which the counterintuitive conclusion above can be overthrown under the rank-dependent expected utility framework, a more general and prominent alternative of the expected utility. Two new criterions of changes in risk, named the monotone probability difference (MPD) and the right monotone probability difference (RMPD) order, are proposed, which is a particular case of the first stochastic dominance. The relationship among MPD, RMPD, and the other two important stochastic orders, monotone likelihood ratio (MLR) and monotone probability ratio (MPR), is examined. A desired comparative statics result is obtained when a shift in the distribution of the risky asset satisfies the RMPD criterion.
机译：众所周知，风险的一阶显性恶化并不一定会导致规避风险的投资者在预期效用框架下减少其对恶化资产的持有量，即使在最简单的投资组合设置中，一个安全资产和一个风险资产也是如此。本文的目的是推导风险资产分配变化的条件，在这种条件下，可以在等级依赖的预期效用框架下推翻上述违反直觉的结论，这是预期效用的更一般，更突出的选择。提出了两种新的风险变化准则，即单调概率差异（MPD）和右单调概率差异（RMPD）顺序，这是第一随机优势的一种特殊情况。检查了MPD，RMPD和其他两个重要的随机顺序之间的关系，即单调似然比（MLR）和单调概率比（MPR）。当风险资产的分布变化满足RMPD标准时，可以获得所需的比较静态结果。

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  • 来源
    《Mathematical Problems in Engineering》 |2013年第14期|784275.1-784275.10|共10页
  • 作者

    Jiangfeng Li; Qiong Wu; Zhiqiang Ye; Shunming Zhang;

  • 作者单位

    School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, China;

    School of Science, Jiujiang University, Jiujiang, Jiangxi 332005, China;

    School of Business, East China University of Science and Technology, Shanghai 200237, China;

    School of Finance, Renmin University of China, Beiiine 100872, China;

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