论文标题
与路径相关的劳动收入的最佳投资组合选择：无限的地平线
Optimal portfolio choice with path dependent labor income: the infinite horizon case
论文作者
论文摘要
我们考虑了一个无限的地平线投资组合问题，并带有借贷限制，其中代理人收到的劳动收入以依赖路径的方式适应金融市场冲击。这种路径依赖性是该模型的新颖性，并导致无限的尺寸随机最佳控制问题。我们完全解决了问题，并以反馈形式明确找到最佳控件。这是可能的，因为即使存在状态约束，我们也能够找到相关的无限尺寸汉密尔顿 - 雅各比 - 贝尔曼（HJB）方程的明确解决方案。据我们所知，这是默顿最佳投资组合问题的第一个无限维度概括，可以找到明确的解决方案。明确的解决方案使我们能够研究最佳策略的特性并讨论其财务影响。
We consider an infinite horizon portfolio problem with borrowing constraints, in which an agent receives labor income which adjusts to financial market shocks in a path dependent way. This path-dependency is the novelty of the model, and leads to an infinite dimensional stochastic optimal control problem. We solve the problem completely, and find explicitly the optimal controls in feedback form. This is possible because we are able to find an explicit solution to the associated infinite dimensional Hamilton-Jacobi-Bellman (HJB) equation, even if state constraints are present. To the best of our knowledge, this is the first infinite dimensional generalization of Merton's optimal portfolio problem for which explicit solutions can be found. The explicit solution allows us to study the properties of optimal strategies and discuss their financial implications.
