Optimal Liquidation with High Risk Aversion and Small Linear Price Impact

Paper: arXiv 2301.01555

Authors: Leonid Dolinskyi, Yan Dolinsky

Abstract

We consider the Bachelier model with linear price impact. Exponential utility indifference prices are studied for vanilla European options in the case where the investor is required to liquidate her position. Our main result is establishing a non-trivial scaling limit for a vanishing price impact which is inversely proportional to the risk aversion. We compute the limit of the corresponding utility indifference prices and find explicitly a family of portfolios which are asymptotically optimal.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents rigorous mathematical analysis of the Bachelier model with linear price impact and high risk aversion, deriving explicit asymptotic optimal strategies. However, it is purely theoretical with no empirical backtesting or real-world market data validation.

Research Flowchart

  flowchart TD
    A["Research Goal: Optimal option liquidation with high risk aversion & small price impact"] --> B["Inputs: Bachelier model, linear price impact, exponential utility"]
    B --> C["Scaling Limit Formulation: Set price impact inversely proportional to risk aversion"]
    C --> D["Utility Indifference Pricing: Solve optimal execution & portfolio allocation"]
    D --> E["Findings: Explicit non-trivial limit prices & asymptotically optimal portfolio family"]