arXiv 2002.033762020-02q-fin.TR

具有Levy过程的Almart-Chriss模型的最优清算轨迹

Optimal liquidation trajectories for the Almgren-Chriss model with Levy processes

Arne Lokka, Junwei Xu

备注：: 36 pages, 2 figures

摘要：

本文在Almante-Chriss框架下考虑了无限期限下的最优清算问题，其中不受影响的资产价格服从Levy过程.临时价格影响由一个满足一定条件的一般函数来描述。我们考虑一个投资者与恒定的绝对风险厌恶，谁想要最大化的期望效用的现金出售他的资产，并表明，这个问题可以减少到一个确定性的优化问题，我们能够明确解决。为了比较我们的结果与指数Levy模型，它提供了一个非常好的统计拟合与观察到的资产价格数据的短期视野，我们得到的（线性）Levy过程近似这样的模型。特别地，我们推导出指数方差-Gamma Levy过程的Levy过程近似的表达式，并研究了相应的最优清算策略的性质。然后，我们提供了一个比较的清算轨迹之间的Levy过程模型和经典的Almante-Chriss模型的合理参数。特别是，我们得到了一个明确的表达式之间的连接的临时影响函数的Levy模型和临时影响函数的布朗运动模型（经典的Almart-Chriss模型），这两个模型的最佳清算轨迹重合。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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