英文标题：
《Optimal Consumption under Habit Formation In Markets with Transaction
Costs and Random Endowments》
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作者：
Xiang Yu
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最新提交年份：
2016
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英文摘要：
This paper studies the optimal consumption under the addictive habit formation preference in markets with transaction costs and unbounded random endowments. To model the proportional transaction costs, we adopt the Kabanov\'s multi-asset framework with a cash account. At the terminal time T, the investor can receive unbounded random endowments for which we propose a new definition of acceptable portfolios based on the strictly consistent price system (SCPS). We prove a type of super-hedging theorem using the acceptable portfolios which enables us to obtain the consumption budget constraint condition under market frictions. Applying the path dependence reduction and the embedding approach, we obtain the existence and uniqueness of the optimal consumption using some auxiliary processes and the duality analysis. As an application of the duality theory, the market isomorphism with special discounting factors is also discussed in the sense that the original optimal consumption with habit formation is equivalent to the standard optimal consumption problem without the habits impact, however, in a modified isomorphic market model.
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中文摘要：
本文研究了具有交易费用和无限随机禀赋的市场中成瘾习惯形成偏好下的最优消费。为了模拟比例交易成本，我们采用了卡巴诺夫的多资产框架和现金账户。在终端时间T，投资者可以获得无限的随机捐赠，我们基于严格一致价格体系（SCPS）提出了可接受投资组合的新定义。我们利用可接受的投资组合证明了一类超套期保值定理，从而得到了市场摩擦下的消费预算约束条件。应用路径依赖约简和嵌入方法，通过一些辅助过程和对偶分析，我们得到了最优消耗的存在性和唯一性。作为对偶理论的一个应用，本文还讨论了具有特殊折扣因子的市场同构问题，即在修正的同构市场模型中，具有习惯形成的原始最优消费等价于没有习惯影响的标准最优消费问题。
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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：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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