论文标题
具有内源参考点和下降约束的消费投资决策
Consumption-investment decisions with endogenous reference point and drawdown constraint
论文作者
论文摘要
我们提出了一种消费投资决策模型，过去的消费峰值$ h $起着至关重要的作用。有两个重要的消费水平：最低约束水平和一个参考水平，在这种水平上，消费率的风险规避。我们解决了这种随机控制问题，并以半明确形式得出了价值功能，最佳消费计划以及最佳投资策略。我们发现五个重要的财富阈值，都是$ h $的功能，其中大多数是非线性功能。从数值结果和理论分析中可以看出，这个直观而简单的模型具有重大的经济影响，至少有三个重要的预测：从财富中消耗的边际倾向通常正在下降，但中等财富水平的趋势可能会增加，并且它与参考点的风险偏见成反比，与风险偏见成反比；隐含的相对风险规避大致是财富的微笑。穷人的福利比富人更容易受到财富冲击的影响。此外，在当地改变风险规避会影响全球最佳策略，从而揭示了一些风险分配行为。
We propose a consumption-investment decision model where past consumption peak $h$ plays a crucial role. There are two important consumption levels: the lowest constrained level and a reference level, at which the risk aversion in terms of consumption rate is changed. We solve this stochastic control problem and derive the value function, optimal consumption plan, and optimal investment strategy in semi-explicit forms. We find five important thresholds of wealth, all as functions of $h$, and most of them are nonlinear functions. As can be seen from numerical results and theoretical analysis, this intuitive and simple model has significant economic implications, and there are at least three important predictions: the marginal propensity to consume out of wealth is generally decreasing but can be increasing for intermediate wealth levels, and it jumps inversely proportional to the risk aversion at the reference point; the implied relative risk aversion is roughly a smile in wealth; the welfare of the poor is more vulnerable to wealth shocks than the wealthy. Moreover, locally changing the risk aversion influences the optimal strategies globally, revealing some risk allocation behaviors.
