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摘要翻译：
本文研究了当市场风险价格为BMO型时，电力效用最大化下的二次半鞅BSDEs。在布朗环境下，我们给出了解存在的充要条件，但证明了唯一性在存在不同平方可积解的连续体的意义下是不成立的。这是因为，与经典的伊藤表示定理相反，用随机指数表示随机变量不是唯一的。本文详细研究了BSDE有界解的情况，导出了一个新的动态指数矩条件，并证明了该条件是一般滤波的最小充分条件。主要结果被几个有趣的例子所补充，这些例子说明了它们的清晰度以及效用最大化BSDE的重要性质。
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英文标题：
《BSDEs in Utility Maximization with BMO Market Price of Risk》
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作者：
Christoph Frei, Markus Mocha and Nicholas Westray
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最新提交年份：
2012
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分类信息：
一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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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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英文摘要：
This article studies quadratic semimartingale BSDEs arising in power utility maximization when the market price of risk is of BMO type. In a Brownian setting we provide a necessary and sufficient condition for the existence of a solution but show that uniqueness fails to hold in the sense that there exists a continuum of distinct square-integrable solutions. This feature occurs since, contrary to the classical Ito representation theorem, a representation of random variables in terms of stochastic exponentials is not unique. We study in detail when the BSDE has a bounded solution and derive a new dynamic exponential moments condition which is shown to be the minimal sufficient condition in a general filtration. The main results are complemented by several interesting examples which illustrate their sharpness as well as important properties of the utility maximization BSDE.
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PDF链接：
https://arxiv.org/pdf/1107.0183
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