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摘要翻译：
考虑了具有随机禀赋过程的约束不完全半鞅市场中的期望消费效用最大化问题，利用凸对偶的技巧建立了一般的存在唯一性结果。将Kramkov和Schachermayer的渐近弹性概念推广到含时情形。通过在时间论证中不对效用函数施加光滑性要求，我们可以在一个共同的框架中处理纯消费和组合消费/最终财富问题。为了使对偶方法成为可能，我们给出了扩大的对偶域的详细刻画，它使人想起将$L^1$扩大到它的拓扑双对偶$(L^{\infty}）^*$,一个有限可加测度空间。作为一个应用，我们讨论了一个有约束的IT流程市场模型的情况。
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英文标题：
《Optimal consumption from investment and random endowment in incomplete
semimartingale markets》
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作者：
Ioannis Karatzas, Gordan Zitkovic
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最新提交年份：
2007
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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 the problem of maximizing expected utility from consumption in a constrained incomplete semimartingale market with a random endowment process, and establish a general existence and uniqueness result using techniques from convex duality. The notion of asymptotic elasticity of Kramkov and Schachermayer is extended to the time-dependent case. By imposing no smoothness requirements on the utility function in the temporal argument, we can treat both pure consumption and combined consumption/terminal wealth problems, in a common framework. To make the duality approach possible, we provide a detailed characterization of the enlarged dual domain which is reminiscent of the enlargement of $L^1$ to its topological bidual $(L^{\infty})^*$, a space of finitely-additive measures. As an application, we treat the case of a constrained It\^ o-process market-model.
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PDF链接：
https://arxiv.org/pdf/0706.0051
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