摘要翻译：
本文研究了不完全半纯市场中具有成瘾习惯形成的消费的连续时间效用最大化问题。通过引入辅助状态过程集和修正的对偶空间，我们将原问题嵌入到乘积空间$\mathbb{L}+^0(\omega\times[0,t],\mathcal{O},\overline{\mathbb{P}}）上的一个具有阴影随机赋值的时间可分离效用最大化问题。利用凸对偶方法建立了最优解的存在唯一性，其中原始值函数定义在两个变量上，即初始财富和初始生活水平。给出了随机折扣过程和效用函数是原优化问题适定性的充分条件。在相同的假设下，当辅助对偶过程不一定是可积的时，凸对偶分析方法中的经典证明可以被修正。
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英文标题：
《Utility maximization with addictive consumption habit formation in
  incomplete semimartingale markets》
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作者：
Xiang Yu
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最新提交年份：
2015
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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：
  This paper studies the continuous time utility maximization problem on consumption with addictive habit formation in incomplete semimartingale markets. Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into a time-separable utility maximization problem with a shadow random endowment on the product space $\mathbb{L}_+^0(\Omega\times [0,T],\mathcal{O},\overline{\mathbb{P}})$. Existence and uniqueness of the optimal solution are established using convex duality approach, where the primal value function is defined on two variables, that is, the initial wealth and the initial standard of living. We also provide sufficient conditions on the stochastic discounting processes and on the utility function for the well-posedness of the original optimization problem. Under the same assumptions, classical proofs in the approach of convex duality analysis can be modified when the auxiliary dual process is not necessarily integrable.
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PDF链接：
https://arxiv.org/pdf/1112.2940