英文标题：
《Investment under Duality Risk Measure》
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作者：
Zuo Quan Xu
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最新提交年份：
2014
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英文摘要：
  One index satisfies the duality axiom if one agent, who is uniformly more risk-averse than another, accepts a gamble, the latter accepts any less risky gamble under the index. Aumann and Serrano (2008) show that only one index defined for so-called gambles satisfies the duality and positive homogeneity axioms. We call it a duality index. This paper extends the definition of duality index to all outcomes including all gambles, and considers a portfolio selection problem in a complete market, in which the agent\'s target is to minimize the index of the utility of the relative investment outcome. By linking this problem to a series of Merton\'s optimum consumption-like problems, the optimal solution is explicitly derived. It is shown that if the prior benchmark level is too high (which can be verified), then the investment risk will be beyond any agent\'s risk tolerance. If the benchmark level is reasonable, then the optimal solution will be the same as that of one of the Merton\'s series problems, but with a particular value of absolute risk aversion, which is given by an explicit algebraic equation as a part of the optimal solution. According to our result, it is riskier to achieve the same surplus profit in a stable market than in a less-stable market, which is consistent with the common financial intuition.
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中文摘要：
一个指数满足二元性公理，如果一个比另一个更倾向于规避风险的代理人接受赌博，后者接受指数下任何风险较小的赌博。Aumann和Serrano（2008）表明，只有一个为所谓的赌博定义的指数满足对偶性和正同质性公理。我们称之为二元指数。本文将对偶指数的定义推广到包括所有赌博在内的所有结果，并考虑一个完全市场中的投资组合选择问题，其中代理人的目标是最小化相对投资结果的效用指数。通过将该问题与一系列类似默顿最优消费的问题联系起来，明确地导出了最优解。研究表明，如果之前的基准水平过高（可以验证），那么投资风险将超出任何代理的风险承受能力。如果基准水平合理，则最优解将与默顿级数问题的最优解相同，但具有特定的绝对风险规避值，该值由作为最优解一部分的显式代数方程给出。根据我们的结果，在稳定的市场中获得相同的盈余利润的风险比在不太稳定的市场中更大，这与常见的金融直觉相一致。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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