The shortfall risk minimization problem for the investor who hedges a contingent claim is studied. It is shown that in case the nonnegativity of the final wealth is not imposed, the optimal strategy in a finite market model is obtained by super-hedging a contingent claim connected with a martingale measure which is a solution of an auxiliary maximization problem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am39-4-2,
author = {Marek Andrzej Koci\'nski},
title = {The martingale method of shortfall risk minimization in a discrete time market},
journal = {Applicationes Mathematicae},
volume = {39},
year = {2012},
pages = {413-424},
zbl = {1254.91724},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-4-2}
}
Marek Andrzej Kociński. The martingale method of shortfall risk minimization in a discrete time market. Applicationes Mathematicae, Tome 39 (2012) pp. 413-424. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-4-2/