### 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 language | English |
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Pages (from-to) | 464-484 |

Number of pages | 21 |

Journal | Mathematical Finance |

Volume | 24 |

Issue number | 3 |

DOIs | |

Publication status | Published - 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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## Cite this

*Mathematical Finance*,

*24*(3), 464-484. https://doi.org/10.1111/mafi.12020