Mean-Variance Hedging with Stochastic Control and BSDEs

Summary

The document develops a method for mean-variance hedging in general semimartingale markets. It frames hedging as a stochastic control problem and establishes that the control problem’s value process has a quadratic form. Three coefficient processes describe that form and are characterized through backward stochastic differential equations (BSDEs).

The coefficient equations provide a way to derive the optimal trading strategy for conditional mean-variance hedging problems. The treatment also gives equivalent formulations intended to connect the approach with earlier research, along with simple illustrative examples. The abstract states the framework and main characterization, but does not report empirical tests or numerical performance. Practical application therefore depends on specifying a market model and solving the relevant equations; the brief description does not detail computational procedures or compare hedging outcomes.

Key ideas

• The hedging problem is formulated as stochastic control for general semimartingale models.
• The value process has a quadratic structure whose three coefficient processes satisfy BSDEs.
• Those coefficient processes can be used to characterize optimal conditional hedging strategies.
• Equivalent BSDE formulations and simple examples connect the method to existing theory.

Tags

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


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









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.