Local risk-minimization for multidimensional assets and payment streams

Martin Schweizer. "Local risk-minimization for multidimensional assets and payment streams." Banach Center Publications 83.1 (2008): 213-229. <http://eudml.org/doc/281822>.

@article{MartinSchweizer2008,
abstract = {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.},
author = {Martin Schweizer},
journal = {Banach Center Publications},
keywords = {local risk-minimization; quadratic hedging; incomplete markets; locally risk-minimizing; Föllmer–Schweizer decomposition; payment streams; structure condition; mean-variance tradeoff},
language = {eng},
number = {1},
pages = {213-229},
title = {Local risk-minimization for multidimensional assets and payment streams},
url = {http://eudml.org/doc/281822},
volume = {83},
year = {2008},
}

TY - JOUR
AU - Martin Schweizer
TI - Local risk-minimization for multidimensional assets and payment streams
JO - Banach Center Publications
PY - 2008
VL - 83
IS - 1
SP - 213
EP - 229
AB - 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.
LA - eng
KW - local risk-minimization; quadratic hedging; incomplete markets; locally risk-minimizing; Föllmer–Schweizer decomposition; payment streams; structure condition; mean-variance tradeoff
UR - http://eudml.org/doc/281822
ER -