论文标题
使用征费过程的Almgren-Chriss模型的最佳清算轨迹
Optimal liquidation trajectories for the Almgren-Chriss model with Levy processes
论文作者
论文摘要
我们考虑了Almgren-Chriss框架中无限视野的最佳清算问题，其中未受影响的资产价格遵循征费过程。临时价格影响由满足某些合理条件的一般功能描述。我们考虑一个具有持续绝对风险的投资者，他想最大限度地利用从他的资产出售中获得的现金的预期效用，并表明该问题可以简化为确定性优化问题，我们能够明确解决。为了将我们的结果与指数征收模型进行比较，该模型在短时间内提供了非常良好的统计拟合，我们得出了此类模型的（线性）征收过程近似。特别是，我们得出了指数方差征税过程的征费过程近似以及相应最佳清算策略的研究特性的表达式。然后，我们提供了清算轨迹的比较，以进行征费过程模型与经典Almgren-Chriss模型之间的合理参数。特别是，我们获得了征费模型的临时影响函数与布朗运动模型的临时影响函数（经典的Almgren-Chriss模型）之间的明确表达，为此，这两个模型的最佳清算轨迹重合。
We consider an optimal liquidation problem with infinite horizon in the Almgren-Chriss framework, where the unaffected asset price follows a Levy process. The temporary price impact is described by a general function which satisfies some reasonable conditions. We consider an investor with constant absolute risk aversion, who wants to maximise the expected utility of the cash received from the sale of his assets, and show that this problem can be reduced to a deterministic optimisation problem which we are able to solve explicitly. In order to compare our results with exponential Levy models, which provides a very good statistical fit with observed asset price data for short time horizons, we derive the (linear) Levy process approximation of such models. In particular we derive expressions for the Levy process approximation of the exponential Variance-Gamma Levy process, and study properties of the corresponding optimal liquidation strategy. We then provide a comparison of the liquidation trajectories for reasonable parameters between the Levy process model and the classical Almgren-Chriss model. In particular, we obtain an explicit expression for the connection between the temporary impact function for the Levy model and the temporary impact function for the Brownian motion model (the classical Almgren-Chriss model), for which the optimal liquidation trajectories for the two models coincide.
