英文标题：
《Optimal Dividend of Compound Poisson Process under a Stochastic Interest
Rate》
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作者：
Linlin Tian, Xiaoyi Zhang
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最新提交年份：
2018
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英文摘要：
In this paper we assume the insurance wealth process is driven by the compound Poisson process. The discounting factor is modelled as a geometric Brownian motion at first and then as an exponential function of an integrated Ornstein-Uhlenbeck process. The objective is to maximize the cumulated value of expected discounted dividends up to the time of ruin. We give an explicit expression of the value function and the optimal strategy in the case of interest rate following a geometric Brownian motion. For the case of the Vasicek model, we explore some properties of the value function. Since we can not find an explicit expression for the value function in the second case, we prove that the value function is the viscosity solution of the corresponding HJB equation.
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中文摘要：
在本文中，我们假设保险财富过程是由复合泊松过程驱动的。首先将贴现因子建模为几何布朗运动，然后将其建模为积分Ornstein-Uhlenbeck过程的指数函数。目标是最大化破产前预期贴现股息的累积价值。在利率服从几何布朗运动的情况下，给出了值函数的显式表达式和最优策略。对于Vasicek模型，我们探讨了值函数的一些性质。由于在第二种情况下找不到值函数的显式表达式，我们证明了值函数是相应HJB方程的粘性解。
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分类信息：

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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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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