论文标题
参考过去的最大支出最佳消费
Optimal Consumption with Reference to Past Spending Maximum
论文作者
论文摘要
本文研究了无限马在指数效用下具有路径依赖参考的最佳消耗。性能是通过非负消费率和最大历史消费的一部分之间的差异来衡量的。运行最大过程的消耗是作为辅助状态过程，因此值函数取决于两个状态变量。汉密尔顿 - 雅各比 - 贝尔曼（HJB）方程可以在不同地区的分段方式启发，以考虑所有约束。通过采用双重变换和平稳拟合原则，得出财富变量的某些阈值，以便可以在每个区域以封闭形式获得HJB方程的经典解决方案和反馈最佳投资和消费策略。提供了验证定理的完整证明，并提供了数值示例，以说明一些财务影响。
This paper studies the infinite-horizon optimal consumption with a path-dependent reference under exponential utility. The performance is measured by the difference between the nonnegative consumption rate and a fraction of the historical consumption maximum. The consumption running maximum process is chosen as an auxiliary state process, and hence the value function depends on two state variables. The Hamilton-Jacobi-Bellman (HJB) equation can be heuristically expressed in a piecewise manner across different regions to take into account all constraints. By employing the dual transform and smooth-fit principle, some thresholds of the wealth variable are derived such that a classical solution to the HJB equation and the feedback optimal investment and consumption strategies can be obtained in closed form in each region. A complete proof of the verification theorem is provided, and numerical examples are presented to illustrate some financial implications.
