CONVEX RISK MEASURES FOR GOOD DEAL BOUNDS |
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Authors: | Takuji Arai Masaaki Fukasawa |
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Affiliation: | 1. Department of Economics, Keio University;2. Department of Mathematics, Osaka University |
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Abstract: | 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. |
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Keywords: | convex risk measure good deal bound Orlicz space risk indifference price fundamental theorem of asset pricing |
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