摘要翻译:
我们考虑一个长期最优投资问题,其中投资者试图使低于目标增长率的概率最小化。从数学观点看,这是一个大偏差控制问题。在足够大的时间范围内,该问题与风险敏感的随机控制问题有关。的确,在我们的定理中,我们在上述两个问题之间的关系中陈述了一个对偶性。此外,在多维线性高斯模型下,我们得到了原问题的显式解。
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英文标题:
《Asymptotics of the probability minimizing a "down-side" risk》
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作者:
Hiroaki Hata, Hideo Nagai, Shuenn-Jyi Sheu
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最新提交年份:
2010
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分类信息:
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: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: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:Quantitative Finance 数量金融学
二级分类:Risk Management 风险管理
分类描述:Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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英文摘要:
We consider a long-term optimal investment problem where an investor tries to minimize the probability of falling below a target growth rate. From a mathematical viewpoint, this is a large deviation control problem. This problem will be shown to relate to a risk-sensitive stochastic control problem for a sufficiently large time horizon. Indeed, in our theorem we state a duality in the relation between the above two problems. Furthermore, under a multidimensional linear Gaussian model we obtain explicit solutions for the primal problem.
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PDF链接:
https://arxiv.org/pdf/1001.2131