## Mean-variance hedging for stochastic volatility models.(English)Zbl 1014.91039

This paper studies financial markets where asset prices $$S$$ are given by Itô type processes whose coefficients depend on an additional stochastic process which is independent of the Brownian motion driving $$S$$ and which lives on a space where one has a martingale representation result. In this situation, the authors characterize the set of equivalent martingale measures $$Q$$ for $$S$$ and give necessary and sufficient conditions for a $$Q$$ to be the variance-optimal martingale measure. This can be used to give explicit expressions in some cases. In addition, the closedness of the space of all stochastic integrals of $$S$$ is also characterized more explicitly.

### MSC:

 91B28 Finance etc. (MSC2000) 60G48 Generalizations of martingales 60H05 Stochastic integrals
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