英文标题：
《Portfolio optimization in the case of an asset with a given liquidation
  time distribution》
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作者：
Ljudmila A. Bordag, Ivan P. Yamshchikov and Dmitry Zhelezov
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最新提交年份：
2014
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英文摘要：
  Management of the portfolios containing low liquidity assets is a tedious problem. The buyer proposes the price that can differ greatly from the paper value estimated by the seller, the seller, on the other hand, can not liquidate his portfolio instantly and waits for a more favorable offer. To minimize losses in this case we need to develop new methods. One of the steps moving the theory towards practical needs is to take into account the time lag of the liquidation of an illiquid asset. This task became especially significant for the practitioners in the time of the global financial crises. Working in the Merton\'s optimal consumption framework with continuous time we consider an optimization problem for a portfolio with an illiquid, a risky and a risk-free asset. While a standard Black-Scholes market describes the liquid part of the investment the illiquid asset is sold at a random moment with prescribed liquidation time distribution. In the moment of liquidation it generates additional liquid wealth dependent on illiquid assets paper value. The investor has the logarithmic utility function as a limit case of a HARA-type utility. Different distributions of the liquidation time of the illiquid asset are under consideration - a classical exponential distribution and Weibull distribution that is more practically relevant. Under certain conditions we show the existence of the viscosity solution in both cases. Applying numerical methods we compare classical Merton\'s strategies and the optimal consumption-allocation strategies for portfolios with different liquidation-time distributions of an illiquid asset.
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中文摘要：
管理包含低流动性资产的投资组合是一个乏味的问题。买方提出的价格可能与卖方估计的账面价值相差很大，而卖方则无法立即清算其投资组合，并等待更优惠的报价。为了最大限度地减少这种情况下的损失，我们需要开发新的方法。将理论推向实际需要的步骤之一是考虑非流动资产清算的时滞。在全球金融危机期间，这项任务对从业人员来说尤为重要。在默顿的连续时间最优消费框架下，我们考虑了一个非流动资产、风险资产和无风险资产组合的优化问题。虽然标准的布莱克-斯科尔斯市场描述了投资的流动部分，但非流动资产是在规定清算时间分布的随机时刻出售的。在清算时，它会根据非流动资产的账面价值产生额外的流动性财富。投资者将对数效用函数作为HARA型效用的极限情况。目前正在考虑非流动资产清算时间的不同分布——更具实际意义的经典指数分布和威布尔分布。在一定条件下，我们证明了两种情况下粘性解的存在性。应用数值方法，我们比较了经典的默顿策略和非流动资产清算时间分布不同的投资组合的最优消费分配策略。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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