CONVEX RISK MEASURES FOR GOOD DEAL BOUNDS
CONVEX RISK MEASURES FOR GOOD DEAL BOUNDS
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DOI：
10.1111/mafi.12020
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发表时间：
2011-08
影响因子：
1.6
通讯作者：
Takuji Arai;M. Fukasawa
中科院分区：
文献类型：
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作者：
Takuji Arai;M. Fukasawa
我们研究了凸风险测度，它描述了一个好的交易界的上界和下界，这是一个无套利定价界的子区间。我们称这样的凸风险测度为好交易估值，并给出了它存在的一组等价条件。一个好的交易估值的特点是几个等价的性质，特别是，我们看到，凸风险度量是一个好的交易估值，只有当它是一个风险无差别价格。最后给出了短缺风险度量的一个应用.此外，我们证明了没有免费午餐（NFL）条件等价于相关凸风险度量的存在性，这是一个很好的交易估值。事实证明，相关性是一笔好交易估值合理的条件。此外，我们还调查了任何好的交易估值相关的条件。
We study convex risk measures describing the upper and lower bounds of a good deal bound, which is a subinterval of a no‐arbitrage pricing bound. We call such a convex risk measure a good deal valuation and give a set of equivalent conditions for its existence in terms of market. A good deal valuation is characterized by several equivalent properties and in particular, we see that a convex risk measure is a good deal valuation only if it is given as a risk indifference price. An application to shortfall risk measure is given. In addition, we show that the no‐free‐lunch (NFL) condition is equivalent to the existence of a relevant convex risk measure, which is a good deal valuation. The relevance turns out to be a condition for a good deal valuation to be reasonable. Further, we investigate conditions under which any good deal valuation is relevant.