One of the earliest concepts for hedging and pricing in incomplete financial markets has been the quadratic criterion of local risk-minimization. However, definitions and theory have so far been established only for the case of a single (one-dimensional) risky asset. We extend the approach to a general multidimensional setting and prove that the basic martingale characterization result for locally risk-minimizing strategies still holds true. In comparison with existing literature, the self-contained presentation is more streamlined, and a number of earlier imposed technical conditions are no longer needed. As a minor extension, we show how payment streams (instead of final payoffs only) can be handled as well.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc83-0-13,
author = {Martin Schweizer},
title = {Local risk-minimization for multidimensional assets and payment streams},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {213-229},
zbl = {1153.91560},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc83-0-13}
}
Martin Schweizer. Local risk-minimization for multidimensional assets and payment streams. Banach Center Publications, Tome 83 (2008) pp. 213-229. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc83-0-13/