英文标题：
《Asymptotic analysis of forward performance processes in incomplete
  markets and their ill-posed HJB equations》
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作者：
Mykhaylo Shkolnikov, Ronnie Sircar, Thaleia Zariphopoulou
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最新提交年份：
2015
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英文摘要：
  We consider the problem of optimal portfolio selection under forward investment performance criteria in an incomplete market. The dynamics of the prices of the traded assets depend on a pair of stochastic factors, namely, a slow factor (e.g. a macroeconomic indicator) and a fast factor (e.g. stochastic volatility). We analyze the associated forward performance SPDE and provide explicit formulae for the leading order and first order correction terms for the forward investment process and the optimal feedback portfolios. They both depend on the investor\'s initial preferences and the dynamically changing investment opportunities. The leading order terms resemble their time-monotone counterparts, but with the appropriate stochastic time changes resulting from averaging phenomena. The first-order terms compile the reaction of the investor to both the changes in the market input and his recent performance. Our analysis is based on an expansion of the underlying ill-posed HJB equation, and it is justified by means of an appropriate remainder estimate.
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中文摘要：
我们研究了不完全市场下，在远期投资绩效准则下的最优投资组合选择问题。交易资产的价格动态取决于一对随机因素，即缓慢因素（如宏观经济指标）和快速因素（如随机波动性）。我们分析了相关的远期绩效SPDE，并为远期投资过程和最优反馈投资组合的前导阶和一阶修正项提供了明确的公式。它们都取决于投资者的初始偏好和动态变化的投资机会。前导阶项类似于它们的时间单调对应项，但具有由平均现象产生的适当随机时间变化。一阶条件汇总了投资者对市场投入变化和近期表现的反应。我们的分析基于基本不适定HJB方程的展开，并通过适当的余数估计证明了其合理性。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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