论文标题
最佳的投资组合选择具有依赖性基准的劳动收入：平均现场模型
Optimal portfolio choice with path dependent benchmarked labor income: a mean field model
论文作者
论文摘要
我们认为，获得劳动收入的代理商面临的生命周期最佳投资组合选择问题，并将其财富分配给有风险的资产，并受到借贷约束的无风险债券。在本文中，为了反映现实的经济环境，我们提出了一个模型，其中劳动收入的动态具有两个主要特征。首先，劳动收入缓慢地调整为金融市场冲击，这是Biffis，E。，Gozzi，F。和Prosdocimi，C。（2020）的一项功能 - “具有依赖路径的劳动收入的最佳投资组合选择：无限的地平线案例”。其次，代理商的劳动收入$ y_i $ $ i $是针对人口$ y^n的劳动收入的基准，$ y^n：=（y_1，y_2，\ ldots，y_n）$ n $代理商具有可比的任务和/或等级。文献中尚未考虑最后一个功能，并且在$ n \ to +\ infty $时面临限制，因此该问题属于无限尺寸麦基恩·弗拉索夫（McKean-Vlasov）的最佳控制家族，这是一个全新且具有挑战性的研究领域。在简化的情况下，我们研究了问题，在这种情况下，添加合适的新变量，我们能够明确找到相关的HJB方程的解决方案并找到最佳反馈控件。
We consider the life-cycle optimal portfolio choice problem faced by an agent receiving labor income and allocating her wealth to risky assets and a riskless bond subject to a borrowing constraint. In this paper, to reflect a realistic economic setting, we propose a model where the dynamics of the labor income has two main features. First, labor income adjust slowly to financial market shocks, a feature already considered in Biffis, E., Gozzi, F. and Prosdocimi, C. (2020) - "Optimal portfolio choice with path dependent labor income: the infinite horizon case". Second, the labor income $y_i$ of an agent $i$ is benchmarked against the labor incomes of a population $y^n:=(y_1,y_2,\ldots,y_n)$ of $n$ agents with comparable tasks and/or ranks. This last feature has not been considered yet in the literature and is faced taking the limit when $n\to +\infty$ so that the problem falls into the family of optimal control of infinite dimensional McKean-Vlasov Dynamics, which is a completely new and challenging research field. We study the problem in a simplified case where, adding a suitable new variable, we are able to find explicitly the solution of the associated HJB equation and find the optimal feedback controls.
