摘要翻译：
本文研究了在由非高斯Ornstein-Uhlenbeck过程驱动的具有随机系数的Black-Scholes金融市场上交易的投资者的最优投资和消费问题。我们假设agent基于幂效用函数进行投资和消费决策。应用通常的变量分离方法，我们面临着求解一个非线性（半线性）一阶偏积分微分方程的问题。通过Feynman-Kac表示导出了一个候选解。利用定义在适当函数空间中的算子的性质，证明了解的唯一性和光滑性。应用一个经典的验证定理来验证最优性。
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英文标题：
《Optimal investment and consumption in a Black--Scholes market with
  L\'evy-driven stochastic coefficients》
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作者：
{\L}ukasz Delong, Claudia Kl\"uppelberg
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最新提交年份：
2008
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分类信息：

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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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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英文摘要：
  In this paper, we investigate an optimal investment and consumption problem for an investor who trades in a Black--Scholes financial market with stochastic coefficients driven by a non-Gaussian Ornstein--Uhlenbeck process. We assume that an agent makes investment and consumption decisions based on a power utility function. By applying the usual separation method in the variables, we are faced with the problem of solving a nonlinear (semilinear) first-order partial integro-differential equation. A candidate solution is derived via the Feynman--Kac representation. By using the properties of an operator defined in a suitable function space, we prove uniqueness and smoothness of the solution. Optimality is verified by applying a classical verification theorem.
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PDF链接：
https://arxiv.org/pdf/0806.2570