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雷达卡
摘要翻译：
我们采用类似于Kallsen和Muhle-Karbe(2010)的影子价格方法，重新考察了Davis和Norman(1990)和Shreve和Soner(1994)的最优投资和消费模型。利用无交易费用模型的完备性，将该奇异随机控制问题的Hamilton-Jacobi-Bellman方程转化为带积分约束的一阶常微分方程的非标准自由边界问题。在证明了自由边界问题有光滑解的基础上，我们利用自由边界问题以一种自包含的方式构造了原最优投资/消费问题的解，而不求助于动态规划原理。此外，我们给出了值函数为有限的模型参数的显式刻画。
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英文标题：
《Shadow prices and well-posedness in the problem of optimal investment
and consumption with transaction costs》
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作者：
Jin Hyuk Choi, Mihai Sirbu, Gordan Zitkovic
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最新提交年份：
2012
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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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英文摘要：
We revisit the optimal investment and consumption model of Davis and Norman (1990) and Shreve and Soner (1994), following a shadow-price approach similar to that of Kallsen and Muhle-Karbe (2010). Making use of the completeness of the model without transaction costs, we reformulate and reduce the Hamilton-Jacobi-Bellman equation for this singular stochastic control problem to a non-standard free-boundary problem for a first-order ODE with an integral constraint. Having shown that the free boundary problem has a smooth solution, we use it to construct the solution of the original optimal investment/consumption problem in a self-contained manner and without any recourse to the dynamic programming principle. Furthermore, we provide an explicit characterization of model parameters for which the value function is finite.
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PDF链接：
https://arxiv.org/pdf/1204.0305
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