英文标题：
《A remark on smooth solutions to a stochastic control problem with a
power terminal cost function and stochastic volatilities》
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作者：
Yal\\c{c}in Aktar, Erik Taflin
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最新提交年份：
2014
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英文摘要：
Incomplete financial markets are considered, defined by a multi-dimensional non-homogeneous diffusion process, being the direct sum of an It\\^{o} process (the price process), and another non-homogeneous diffusion process (the exogenous process, representing exogenous stochastic sources). The drift and the diffusion matrix of the price process are functions of the time, the price process itself and the exogenous process. In the context of such markets and for power utility functions, it is proved that the stochastic control problem consisting of optimizing the expected utility of the terminal wealth, has a classical solution (i.e. $C^{1,2}$). This result paves the way to a study of the optimal portfolio problem in incomplete forward variance stochastic volatility models, along the lines of Ref: Ekeland et al.
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中文摘要：
不完全金融市场被认为是由一个多维非齐次扩散过程定义的，它是一个It \\{o}过程（价格过程）和另一个非齐次扩散过程（外生过程，代表外生随机源）的直接和。价格过程的漂移和扩散矩阵是时间、价格过程本身和外生过程的函数。在这样的市场和电力效用函数的背景下，证明了由优化终端财富的预期效用组成的随机控制问题有一个经典解（即$C^{1,2}$）。这一结果为研究不完全前向方差随机波动模型中的最优投资组合问题铺平了道路，参考文献：Ekeland等人。
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分类信息：

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：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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