On the Structure of General Mean-Variance Hedging Strategies

Abstract

We provide a new characterisation of mean-variance hedging strategies in a general semimartingale market. The key point is the introduction of a new probability measure P* which turns the dynamic asset allocation problem into a myopic one. The minimal martingale measure relative to P* coincides with the variance-optimal martingale measure relative to the original probability measure P.

Keywords: mean-variance hedging, opportunity process, opportunity-neutral measure, incomplete market, Sharpe ratio, semimartingales

JEL Classification: G11, G12, G13