Risk Aversion and the Dynamics of Optimal Liquidation Strategies in Illiquid Markets
17 Pages Posted: 11 Feb 2008
Date Written: February 8, 2008
Abstract
We consider the infinite-horizon optimal portfolio liquidation problem for a von Neumann-Morgenstern investor in the liquidity model of Almgren (2003). Using a stochastic control approach, we characterize the value function and the optimal strategy as classical solutions of nonlinear parabolic partial differential equations. We furthermore analyze the sensitivities of the value function and the optimal strategy with respect to the various model parameters. In particular, we find that the optimal strategy is aggressive or passive in-the-money, respectively, if and only if the utility function displays increasing or decreasing risk aversion. Surprisingly, only few further monotonicity relations exist with respect to the other parameters. We point out in particular that the speed by which the remaining asset position is sold can be decreasing in the size of the position but increasing in the liquidity price impact.
Keywords: Liquidity, illiquid markets, optimal liquidation strategies, dynamic trading strategies, algorithmic trading, utility maximization
JEL Classification: G10, G12, G14, G20, G33
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
Optimal Trading Strategy and Supply/Demand Dynamics
By Anna A. Obizhaeva and Jiang Wang
-
Optimal Trading Strategy and Supply/Demand Dynamics
By Anna A. Obizhaeva and Jiang Wang
-
Optimal Trading Strategy and Supply/Demand Dynamics
By Anna A. Obizhaeva and Jiang Wang
-
Optimal Execution Strategies in Limit Order Books with General Shape Functions
By Aurélien Alfonsi, Antje Fruth, ...
-
By Olaf Korn and Alexander Kempf
-
Quasi-Arbitrage and Price Manipulation
By Gur Huberman and Werner Stanzl
-
Fluctuations and Response in Financial Markets: The Subtle Nature of 'Random' Price Changes
By Jean-philippe Bouchaud, Yuval Gefen, ...
-
By Gur Huberman and Werner Stanzl
-
How Markets Slowly Digest Changes in Supply and Demand
By Jean-philippe Bouchaud, J. Doyne Farmer, ...
-
No-Dynamic-Arbitrage and Market Impact
By Jim Gatheral