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CONVEX RISK MEASURES FOR GOOD DEAL BOUNDS
Author(s) -
Arai Takuji,
Fukasawa Masaaki
Publication year - 2014
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12020
Subject(s) - valuation (finance) , regular polygon , risk measure , mathematics , upper and lower bounds , mathematical economics , coherent risk measure , econometrics , arbitrage , measure (data warehouse) , economics , actuarial science , mathematical optimization , computer science , financial economics , finance , portfolio , mathematical analysis , geometry , database
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.