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Optimal Portfolio Choice with Path Dependent Labor Income: the Infinite Horizon Case
SIAM Journal on Control and Optimization ( IF 2.2 ) Pub Date : 2020-07-08 , DOI: 10.1137/19m1259687
Enrico Biffis , Fausto Gozzi , Cecilia Prosdocimi

SIAM Journal on Control and Optimization, Volume 58, Issue 4, Page 1906-1938, January 2020.
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 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.


中文翻译:

路径依赖劳动收入的最优投资组合选择:无限期案例

SIAM控制与优化杂志,第58卷,第4期,第1906-1938页,2020年1月。
我们考虑一个带有借款约束的无限期投资组合问题,其中代理商获得劳动收入,该收入以依赖于路径的方式适应金融市场的冲击。这种路径依赖性是模型的新颖性,并导致无限维随机最优控制问题。我们完全解决了问题,并以反馈形式明确找到了最优控制。这是可能的,因为即使存在状态约束,我们也能够找到相关联的无限维HJB方程的显式解。据我们所知,这是默顿最优投资组合问题的第一个无穷维概括,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属性并讨论其财务含义。
更新日期:2020-07-23
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