Convex risk measures for good deal bounds

Takuji Arai, Masaaki Fukasawa

Research output: Contribution to journalArticle

9 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)464-484
Number of pages21
JournalMathematical Finance
Volume24
Issue number3
DOIs
Publication statusPublished - 2014 Jul

Keywords

  • Convex risk measure
  • Fundamental theorem of asset pricing
  • Good deal bound
  • Orlicz space
  • Risk indifference price

ASJC Scopus subject areas

  • Accounting
  • Finance
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Applied Mathematics

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