Dual Methods for Utility Hedging with Quadratic Trading Costs

Summary

The paper studies portfolio choice when trades incur quadratic costs and any remaining position must be closed at a fixed horizon. Its central contribution is a duality result for maximizing exponential utility under those constraints. The dual perspective provides a way to analyze the constrained trading problem and is then applied to hedging in a Bachelier price model.

For European claims whose payoff is quadratic, the paper derives an explicit optimal trading strategy. The supplied description does not give the formula, assumptions beyond the stated model features, or numerical tests, so it does not establish how the strategy performs in practice or how the result extends to other payoff shapes, price dynamics, or cost structures.

Key ideas

• The analysis combines exponential utility with quadratic costs for trading.
• A terminal liquidation requirement is part of the investor’s optimization problem.
• A duality result is used to study utility-based hedging in a Bachelier model.
• An explicit optimal strategy is obtained for European claims with quadratic payoffs.
• The description provides no numerical evaluation or stated extension to other claim types.

Tags

# Duality Theory for Exponential Utility--Based Hedging in the Almgren--Chriss Model


# Duality Theory for Exponential Utility--Based Hedging in the Almgren--Chriss Model









In this paper, we obtain a duality result for the exponential utility maximization problem where trading is subject to quadratic transaction costs and the investor is required to liquidate her position at the maturity date. As an application of the duality, we treat utility-based hedging in the Bachelier model. For European contingent claims with a quadratic payoff, we compute explicitly the optimal trading strategy.

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