Optimal Liquidation of an Asset under Drift Uncertainty
Optimal Liquidation of an Asset under Drift Uncertainty
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DOI：
10.1137/15m1033265
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发表时间：
2015-09
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影响因子：
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通讯作者：
Erik Ekström;Juozas Vaicenavicius
中科院分区：
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作者：
Erik Ekström;Juozas Vaicenavicius
我们研究寻找最佳停止策略来清算漂移未知的资产的问题。采用贝叶斯方法，我们通过允许任意概率分布来表征漂移参数的不确定性来模拟个体对漂移参数的初始信念。过滤理论用于描述观察价格过程后关于漂移的后验信念的演变。最佳停止时间被确定为后验均值低于单调边界的第一次通过时间，其可以表征为非线性积分方程的唯一解。我们还研究先验分布和资产波动性的单调性。
We study a problem of finding an optimal stopping strategy to liquidate an asset with unknown drift. Taking a Bayesian approach, we model the initial beliefs of an individual about the drift parameter by allowing an arbitrary probability distribution to characterise the uncertainty about the drift parameter. Filtering theory is used to describe the evolution of the posterior beliefs about the drift once the price process is being observed. An optimal stopping time is determined as the first passage time of the posterior mean below a monotone boundary, which can be characterised as the unique solution to a non-linear integral equation. We also study monotonicity properties with respect to the prior distribution and the asset volatility.