Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/278247 
Year of Publication: 
2022
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 671
Publisher: 
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
Abstract: 
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.
Subjects: 
Optimal timing of health investment
Optimal consumption
Optimal portfolio choice
Duality
Optimal stopping
Free boundary
Stochastic control
JEL: 
G11
E21
I13
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Working Paper

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