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

Biagini, Francesca; Guasoni, Paolo; Pratelli, Maurizio

Math. Finance 10, No. 2, 109-123 (2000).

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.

Reviewer: Martin Schweizer (München)

MSC:

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

Keywords:

mean-variance hedging; stochastic volatility; variance-optimal martingale measure