Robust Mean-Variance Hedging with Misspecified Volatility

Summary

This work addresses mean-variance hedging when markets are incomplete, information may have an arbitrary structure, and asset-price volatility is misspecified. It describes a robust trading strategy for hedging a contingent claim, with the asset price modeled as a multidimensional continuous semimartingale. The approach is paired with construction of an optimal robust estimate for an unknown multidimensional parameter in the drift of a diffusion process with small noise.

The results are applied to a stochastic-volatility setting in which latent volatility follows a process with an unknown drift parameter and a small diffusion term. This frames hedging and parameter uncertainty together, rather than assuming the volatility specification is known exactly. The supplied description does not give the strategy's explicit formula, assumptions in detail, numerical comparisons, or empirical performance, so it supports understanding the modeling aim but not judging practical effectiveness or implementation requirements.

Key ideas

• The proposed strategy hedges contingent claims by minimizing mean-variance error in an incomplete market.
• The asset price is modeled as a multidimensional continuous semimartingale with potentially misspecified volatility.
• An optimal robust estimate addresses an unknown multidimensional drift parameter in a small-noise diffusion.
• The framework is applied to stochastic volatility with latent dynamics and parameter uncertainty.
• The description does not provide empirical evidence or enough detail to assess implementation performance.

Tags

# Optimal Robust Mean-Variance Hedging in Incomplete Financial Markets


# Optimal Robust Mean-Variance Hedging in Incomplete Financial Markets









Optimal B-robust estimate is constructed for multidimensional parameter in drift coefficient of diffusion type process with small noise. Optimal mean-variance robust (optimal V -robust) trading strategy is find to hedge in mean-variance sense the contingent claim in incomplete financial market with arbitrary information structure and misspecified volatility of asset price, which is modelled by multidimensional continuous semimartingale. Obtained results are applied to stochastic volatility model, where the model of latent volatility process contains unknown multidimensional parameter in drift coefficient and small parameter in diffusion term.

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