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Local risk-minimization for multidimensional assets and payment streams. (English) Zbl 1153.91560

Stettner, Łukasz (ed.), Advances in mathematics of finance. Contributed papers of the 2nd general AMaMeF (advanced mathematical methods of finance) conference and Banach Center conference on advances in mathematics of finance, Bȩdlewo, Poland, April 30–May 5, 2007. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 83, 213-229 (2008).
Summary: 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.
For the entire collection see [Zbl 1151.91009].

MSC:

91G10 Portfolio theory
60G48 Generalizations of martingales
60G35 Signal detection and filtering (aspects of stochastic processes)
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