On the Structure of General Mean-Variance Hedging Strategies

TL;DR

This paper introduces a new probability measure to characterize mean-variance hedging strategies in general markets, simplifying the dynamic problem to a myopic one and linking it to the variance-optimal measure.

Contribution

It provides a novel measure-based framework that unifies mean-variance hedging with martingale measures in semimartingale markets.

Findings

The new measure $P^{ullet}$ simplifies the hedging problem.

The minimal martingale measure under $P^{ullet}$ matches the variance-optimal measure.

The approach applies to general semimartingale market models.

Abstract

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