摘要翻译:
在无摩擦市场中,效用最大化问题通常用随机控制或鞅方法来解决。从Davis和Norman的开创性论文[Math.Oper.Res.15(1990)676-713]开始,随机控制理论也被用来解决存在比例交易费用的各种此类问题。另一方面,鞅方法到目前为止只用于导出一般的结构结果。这些理论将无摩擦市场的对偶理论应用于真实价格过程的买卖界内的虚拟影子价格过程。在本文中,我们证明了这种对偶方法实际上既可用于导出对数效用和比例交易费用的Merton问题的候选解,也可用于验证。特别地,我们确定影子价格过程。
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英文标题:
《On using shadow prices in portfolio optimization with transaction costs》
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作者:
J. Kallsen, J. Muhle-Karbe
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最新提交年份:
2010
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分类信息:
一级分类:Quantitative Finance 数量金融学
二级分类:Computational Finance 计算金融学
分类描述:Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法,包括蒙特卡罗,偏微分方程,格子和其他数值方法,并应用于金融建模
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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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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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英文摘要:
In frictionless markets, utility maximization problems are typically solved either by stochastic control or by martingale methods. Beginning with the seminal paper of Davis and Norman [Math. Oper. Res. 15 (1990) 676--713], stochastic control theory has also been used to solve various problems of this type in the presence of proportional transaction costs. Martingale methods, on the other hand, have so far only been used to derive general structural results. These apply the duality theory for frictionless markets typically to a fictitious shadow price process lying within the bid-ask bounds of the real price process. In this paper, we show that this dual approach can actually be used for both deriving a candidate solution and verification in Merton's problem with logarithmic utility and proportional transaction costs. In particular, we determine the shadow price process.
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PDF链接:
https://arxiv.org/pdf/1010.4989