摘要翻译：
考虑了一个由扩散过程驱动的随机系数Black-Scholes金融市场的最优投资和消费问题。我们假设一个agent基于CRRA效用函数进行消费和投资决策。利用动态规划方法研究了Hamilton-Jacobi-Bellman(HJB)方程，这是一个高度非线性的第二类偏微分方程(PDE)。利用Feynman-Kac表示，证明了解的唯一性和光滑性。此外，我们还研究了迭代数值格式对价值函数和最优投资组合的最优收敛速度。我们证明，在这种情况下，最优收敛速度是超几何的，即比任何几何的收敛速度都快。我们将我们的结果应用于随机波动的金融市场。
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英文标题：
《Optimal consumption and investment for markets with random coefficients》
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作者：
Berdjane Belkacem, Serguei Pergamenchtchikov (LMRS)
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最新提交年份：
2011
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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：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：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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英文摘要：
  We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic coefficients driven by a diffusion process. We assume that an agent makes consumption and investment decisions based on CRRA utility functions. The dynamical programming approach leads to an investigation of the Hamilton Jacobi Bellman (HJB) equation which is a highly non linear partial differential equation (PDE) of the second oder. By using the Feynman - Kac representation we prove uniqueness and smoothness of the solution. Moreover, we study the optimal convergence rate of the iterative numerical schemes for both the value function and the optimal portfolio. We show, that in this case, the optimal convergence rate is super geometrical, i.e. is more rapid than any geometrical one. We apply our results to a stochastic volatility financial market.
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PDF链接：
https://arxiv.org/pdf/1102.1186