随机双曲折现下的消费与最优投资策略探究

数学理论与应用 ›› 2020, Vol. 40 ›› Issue (3): 85-93.

随机双曲折现下的消费与最优投资策略探究

侯木舟¹，陈英皞^1，*，季书屹^1，余涵钰²，杨迪¹

1.中南大学数学与统计学院，湖南长沙，410083
2.中南大学商学院，湖南长沙，410083

出版日期:2020-09-30 发布日期:2021-06-15

Research on Consumption and Optimal Investment Strategies Based on Hyperbolic Discount Method

Online:2020-09-30 Published:2021-06-15

摘要/Abstract

摘要：

在本文中，我们主要讨论了随机双曲折现中，假设投资者的消费行为是一个布朗运动时，其用于投资风险资产的最优投资额。基于汉密尔顿-雅克比-贝尔曼方程计算常数绝对风险厌恶型投资者的效用函数下的最优投资组合，并给出了这组方程的近似解。在此基础上，我们分析了当消费服从Wiener过程时风险资产投资的一些重要性质，研究了消费行为与风险资产投资行为之间的关系。

关键词:

双曲折现, 随机过程, 投资组合

Abstract:

In this article, we mainly discuss the optimal amount of investment for risky assets in stochastic hyperbolic discounting, assuming that investors’ consumption behavior is a Brownian motion. Based on the Hamilton-Jacobi-Bellman equation, the optimal investment portfolio with the constant absolute risk aversion investor is calculated, and the approximate solution of equation is given. Moreover, we analyzed some important properties of risky asset investment when consumption obeys the Wiener process, and then studied the relationship between consumption behavior and risky asset investment behavior.

Key words:

hyperbolic discounting, stochastic process, portfolio

侯木舟, 陈英皞, 季书屹, 余涵钰, 杨迪.

随机双曲折现下的消费与最优投资策略探究 [J]. 数学理论与应用, 2020, 40(3): 85-93.