Convex risk measures for good deal bounds
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.
Keywords
Cite
@article{arxiv.1108.1273,
title = {Convex risk measures for good deal bounds},
author = {Takuji Arai and Masaaki Fukasawa},
journal= {arXiv preprint arXiv:1108.1273},
year = {2011}
}