Consumption decision, portfolio choice and healthcare irreversible investment

Arbeitspapier

We propose a tractable dynamic framework for the joint determination of optimal consumption, portfolio choice, and healthcare irreversible investment. Our model is based on a Merton's portfolio and consumption problem, where, in addition, the agent can choose the time at which undertaking a costly lump sum health investment decision. Health depreciates with age and directly affects the agent's mortality force, so that investment into healthcare reduces the agent's mortality risk. The resulting optimization problem is formulated as a stochastic control-stopping problem with a random time-horizon and state-variables given by the agent's wealth and health capital. We transform this problem into its dual version, which is now a two-dimensional optimal stopping problem with interconnected dynamics and finite time-horizon. Regularity of the optimal stopping value function is derived and the related free boundary surface is proved to be Lipschitz continuous and it is characterized as the unique solution to a nonlinear integral equation. In the original coordinates, the agent thus invests into healthcare whenever her wealth exceeds an age- and health-dependent transformed version of the optimal stopping boundary.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Center for Mathematical Economics Working Papers ; No. 671

Classification and Topics

• Classification: Wirtschaft ; Portfolio Choice; Investment Decisions ; Macroeconomics: Consumption; Saving; Wealth ; Health Insurance, Public and Private
• Subject: Optimal timing of health investment ; Optimal consumption ; Optimal portfolio choice ; Duality ; Optimal stopping ; Free boundary ; Stochastic control

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Ferrari, Giorgio ; Zhu, Shihao
• Event: Veröffentlichung
• (who): Bielefeld University, Center for Mathematical Economics (IMW)
• (where): Bielefeld
• (when): 2022

Further information

• Handle: http://hdl.handle.net/10419/278247
• URN: urn:nbn:de:0070-pub-29675370
• Last update: 10.03.2025, 11:43 AM CET