最优投资组合选择中的工资刚性与退休

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2025-03-18 DOI:10.1016/j.automatica.2025.112225

Sara Biagini , Enrico Biffis , Fausto Gozzi , Margherita Zanella

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引用次数: 0

摘要

研究了具有随机劳动收入、借款约束和有限退休日期的代理人的生命周期投资组合选择问题。与Biffis等人（2020）类似，工资以路径依赖的方式发展，但有限退休时间的存在导致了一个新的两阶段无限维随机最优控制问题，该问题具有反馈形式的显式最优控制。我们找到了相关的Hamilton-Jacobi-Bellman （HJB）方程的显式解，该方程是一个无限维抛物型偏微分方程。由于存在时间相关的状态约束，最优反馈的识别是微妙的，这在无限维随机控制文献中似乎是新的。显式解允许我们研究最优策略的性质，并讨论其对投资组合选择的影响。与具有马尔可夫动态的模型相反，路径依赖现在可以调节由人力资本中隐含的风险资产持有引起的对冲需求，从而导致与工资刚性一致的更丰富的资产配置预测，并且代理了解他们的收入潜力。

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Wage rigidity and retirement in optimal portfolio choice

We study an agent’s lifecycle portfolio choice problem with stochastic labor income, borrowing constraints and a finite retirement date. Similarly to Biffis et al. (2020), wages evolve in a path-dependent way, but the presence of a finite retirement time leads to a novel, two-stage infinite dimensional stochastic optimal control problem with explicit optimal controls in feedback form. We find an explicit solution to the associated Hamilton–Jacobi–Bellman (HJB) equation, which is an infinite dimensional PDE of parabolic type. The identification of the optimal feedbacks is delicate due to the presence of time-dependent state constraints, which appear to be new in the infinite dimensional stochastic control literature. The explicit solution allows us to study the properties of optimal strategies and discuss their implications for portfolio choice. As opposed to models with Markovian dynamics, path dependency can now modulate the hedging demand arising from the implicit holding of risky assets in human capital, leading to richer asset allocation predictions consistent with wage rigidity and the agents learning about their earning potential.

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来源期刊

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.