英文标题：
《Deterministic Income with Deterministic and Stochastic Interest Rates》
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作者：
Julia Eisenberg
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最新提交年份：
2016
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英文摘要：
We consider an individual or household endowed with an initial capital and an income, modeled as a deterministic process with a continuous drift rate. At first, we model the discounting rate as the price of a zero-coupon bond at zero under the assumption of a short rate evolving as an Ornstein-Uhlenbeck process. Then, a geometric Brownian motion as the preference function and an Ornstein-Uhlenbeck process as the short rate are taken into consideration. It is assumed that the primal interest of the economic agent is to maximise the cumulated value of (expected) discounted consumption from a given time up to a finite deterministic time horizon $T\\in\\R_+$ or, in a stochastic setting, infinite time horizon. We find an explicit expression for the value function and for the optimal strategy in the first two cases. In the third case, we have to apply the viscosity ansatz.
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中文摘要：
我们考虑一个拥有初始资本和收入的个人或家庭，将其建模为具有连续漂移率的确定性过程。首先，在短期利率演化为Ornstein-Uhlenbeck过程的假设下，我们将贴现率建模为零息票债券的价格。然后，以几何布朗运动为偏好函数，以Ornstein-Uhlenbeck过程为短速率。假设经济主体的首要利益是最大化从给定时间到有限确定性时间范围$T\\in\\R\\u+$的（预期）折扣消费的累积价值，或在随机环境下，无限时间范围。在前两种情况下，我们找到了值函数和最优策略的显式表达式。在第三种情况下，我们必须应用粘度ansatz。
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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：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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