Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets |
| |
Authors: | Alexander Schied Torsten Schöneborn |
| |
Institution: | (1) School of ORIE, Cornell University, 232 Rhodes Hall, Ithaca, NY 14853, USA;(2) Deutsche Bank Quantitative Products Laboratory, Technical University Berlin, Alexanderstr. 5, 10178 Berlin, Germany;(3) AHL Research, Man Investments Ltd Sugar Quay, Lower Thames Street, London, EC3R 6DU, UK |
| |
Abstract: | We consider the infinite-horizon optimal portfolio liquidation problem for a von Neumann–Morgenstern investor in the liquidity
model of Almgren (Appl. Math. Finance 10:1–18, 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: | Optimal liquidation Optimal trade execution Aggressive in the money Passive in the money Liquidity risk Market impact Absolute risk aversion Hamilton– Jacobi– Bellman equation Nonlinear partial differential equation Sensitivity analysis |
本文献已被 SpringerLink 等数据库收录! |
|