Change of filtrations and mean–variance hedging

Abstract

We consider the mean–variance hedging (MVH) problem (under measure P) of two kinds of investors for two different levels of information, described by two filtrations and such that . Under the assumption that there exists a measure such that all -martingales are -martingales, we give the variance-optimal martingale measure (VOMM) with respect to and through a couple of stochastic Riccati equation (SRE)s, which can be viewed as the same SRE with differential terminal value under . Then we derive an explicit form of the optimal mean–variance strategy and the optimal costs with respect to and . We describe the concept of -no-value-to-investment in the means of mean–variance, and for a given contingent claim , we compare their optimal costs with respect to and .