Optimal Liquidation by a Large Investor

Abstract. We develop a partial equilibrium model to investigate the problem of optimal liquidation over a finite or infinite time horizon for an investor with large holdings in a risky asset. The imperfect liquidity in the market for the asset leads to a nonlinear path dependent feedback on the underlying asset price process due to the large investor's trades and his holdings in the asset. We use probabilistic techniques to prove verification and existence results for optimal liquidation policies for the utility-maximizing investor under broad assumptions. In particular, our results imply the existence of optimal policies if the investor has power utility functions. We provide analytical expressions for the optimal policy when the large investor has logarithmic preferences. We use these results to characterize the "liquidity discount," which is a measure of the liquidity risk of the large investor's position in the risky asset. Key words. liquidation, large investor...

• Type: Journal
• Year: 2008
• Where: SIAMAM
• Authors: Ajay Subramanian
• Keywords: Asset, Large Investors, Optimal Liquidation, SIAMAM 2008