Local risk-minimization for multidimensional assets and payment streams

Volume 83 / 2008

Martin Schweizer Banach Center Publications 83 (2008), 213-229 MSC: Primary 91B28; Secondary 60G48, 60G35. DOI: 10.4064/bc83-0-13


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.


  • Martin SchweizerETH Zürich, Departement Mathematik
    ETH-Zentrum, HG G 51.2
    CH-8092 Zürich, Switzerland

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