Optimal liquidation under stochastic liquidity

被引:28
|
作者
Becherer, Dirk [1 ]
Bilarev, Todor [1 ]
Frentrup, Peter [1 ]
机构
[1] Humboldt Univ, Inst Math, Unter Linden 6, D-10099 Berlin, Germany
关键词
Stochastic liquidity; Transient price impact; Optimal liquidation; Stochastic volume effect; Singular control; Finite-fuel problem; Free boundary; Inverse local time; Elastic reflection; TRANSIENT PRICE IMPACT; EXECUTION STRATEGIES;
D O I
10.1007/s00780-017-0346-2
中图分类号
F8 [财政、金融];
学科分类号
0202 ;
摘要
We solve explicitly a two-dimensional singular control problem of finite fuel type for an infinite time horizon. The problem stems from the optimal liquidation of an asset position in a financial market with multiplicative and transient price impact. Liquidity is stochastic in that the volume effect process, which determines the intertemporal resilience of the market in the spirit of Predoiu et al. (SIAM J. Financ. Math. 2:183-212, 2011), is taken to be stochastic, being driven by its own random noise. The optimal control is obtained as the local time of a diffusion process reflected at a non-constant free boundary. To solve the HJB variational inequality and prove optimality, we need a combination of probabilistic arguments and calculus of variations methods, involving Laplace transforms of inverse local times for diffusions reflected at elastic boundaries.
引用
收藏
页码:39 / 68
页数:30
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