摘要翻译：
当当前效用也依赖于财富过程时，我们考虑了一个投资-消费组合的效用最大化问题。这类问题的出现，例如，在具有随机期限或随机交易时间的投资组合优化中。为了克服这个问题的困难，我们采用了双重方法。定义了一个对偶问题，并用动态规划的方法对其进行处理，证明了相应的Hamilton-Jacobi-Bellman方程的粘性解属于一类适当的光滑函数。由此定义了原Hamilton-Jacobi-Bellman方程的光滑解，证明了该解在适当的类中确实是唯一的，并且与原问题的值函数一致。给出了结果的一些金融应用。
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英文标题：
《Utility maximization with current utility on the wealth: regularity of
  solutions to the HJB equation》
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作者：
Salvatore Federico, Paul Gassiat, Fausto Gozzi
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最新提交年份：
2015
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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 consider a utility maximization problem for an investment-consumption portfolio when the current utility depends also on the wealth process. Such kind of problems arise, e.g., in portfolio optimization with random horizon or with random trading times. To overcome the difficulties of the problem we use the dual approach. We define a dual problem and treat it by means of dynamic programming, showing that the viscosity solutions of the associated Hamilton-Jacobi-Bellman equation belong to a suitable class of smooth functions. This allows to define a smooth solution of the primal Hamilton-Jacobi-Bellman equation, proving that this solution is indeed unique in a suitable class and coincides with the value function of the primal problem. Some financial applications of the results are provided.
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PDF链接：
https://arxiv.org/pdf/1301.0280