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摘要翻译：
在一般半鞅金融模型中，考虑一个效用最大化问题，每个风险资产的持股数量受到约束。这些约束由可预测的凸集值过程建模，其值不一定包含原点；也就是说，投资者不持有任何风险投资可能是不允许的。这种设置包含了经典的约束效用最大化问题，以及存在非流动性资产或随机禀赋的问题。我们的主要结果证明了在效用函数没有光滑性要求的情况下，这类模型中最优交易策略的存在性。结果还表明，对偶优化问题可以在一组可数可加的概率测度上提出，从而避免了通常的有限可加的扩大。
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英文标题：
《On utility maximization under convex portfolio constraints》
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作者：
Kasper Larsen, Gordan \v{Z}itkovi\'c
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最新提交年份：
2013
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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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一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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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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英文摘要：
We consider a utility-maximization problem in a general semimartingale financial model, subject to constraints on the number of shares held in each risky asset. These constraints are modeled by predictable convex-set-valued processes whose values do not necessarily contain the origin; that is, it may be inadmissible for an investor to hold no risky investment at all. Such a setup subsumes the classical constrained utility-maximization problem, as well as the problem where illiquid assets or a random endowment are present. Our main result establishes the existence of optimal trading strategies in such models under no smoothness requirements on the utility function. The result also shows that, up to attainment, the dual optimization problem can be posed over a set of countably-additive probability measures, thus eschewing the need for the usual finitely-additive enlargement.
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PDF链接：
https://arxiv.org/pdf/1102.0346
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