Electronic Resource
Boston, USA and Oxford, UK
:
Blackwell Publishers Inc
Mathematical finance
8 (1998), S. 0
ISSN:
1467-9965
Source:
Blackwell Publishing Journal Backfiles 1879-2005
Topics:
Mathematics
,
Economics
Notes:
We consider the mean-variance hedging problem when the risky assets price process is a continuous semimartingale. The usual approach deals with self-financed portfolios with respect to the primitive assets family. By adding a numéraire as an asset to trade in, we show how self-financed portfolios may be expressed with respect to this extended assets family, without changing the set of attainable contingent claims.We introduce the hedging numéraire and relate it to the variance-optimal martingale measure. Using this numéraire both as a deflator and to extend the primitive assets family, we are able to transform the original mean-variance hedging problem into an equivalent and simpler one; this transformed quadratic optimization problem is solved by the Galtchouk–Kunita–Watanabe projection theorem under a martingale measure for the hedging numéraire extended assets family. This gives in turn an explicit description of the optimal hedging strategy for the original mean-variance hedging problem.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1111/1467-9965.00052
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