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The use of gain-loss ratio as a measure of attractiveness has been
introduced by Bernardo and Ledoit. In their well-known paper, they
show that gain-loss ratio restrictions have a dual representation in
terms of restricted pricing kernels.
In spite of its clear financial significance, gain-loss ratio has
been largely ignored in the mathematical finance literature, with few
exceptions (Cherny and Madan, Pinar). The main reason is intrinsic
lack of good mathematical properties. This paper aims to be a
rigorous study of gain-loss ratio and its dual representations
in a continuous-time market setting, placing it in the context of
risk measures and acceptability indexes. We also point out (and
correctly reformulate) an erroneous statement made by Bernardo and
Ledoit in their main result. This is joint work with M. Pinar.