Mean-variance hedging via stochastic control and BSDEs for general semimartingales

TL;DR

This paper develops a stochastic control approach using BSDEs to solve mean-variance hedging problems in general semimartingale models, providing a quadratic value process and explicit optimal strategies.

Contribution

It introduces a novel method linking stochastic control and BSDEs for mean-variance hedging in broad semimartingale settings, with explicit characterizations and examples.

Findings

Quadratic structure of the value process identified

Coefficient processes characterized by BSDEs

Explicit optimal trading strategies derived

Abstract

We solve the problem of mean-variance hedging for general semimartingale models via stochastic control methods. After proving that the value process of the associated stochastic control problem has a quadratic structure, we characterize its three coefficient processes as solutions of semimartingale backward stochastic differential equations and show how they can be used to describe the optimal trading strategy for each conditional mean-variance hedging problem. For comparison with the existing literature, we provide alternative equivalent versions of the BSDEs and present a number of simple examples.