Overview
This research presents a dynamic framework designed to analyze optimal consumption, portfolio selection, and irreversible healthcare investment, extending Merton's classical portfolio and consumption problem. The model integrates the concept of an agent undertaking healthcare investment at a continuous rate, where health capital depreciates with age and directly influences the agent's force of mortality. Investment in healthcare is thus posited to reduce mortality risk.
Research Context
The study builds upon Merton's portfolio and consumption problem by introducing an additional mechanism for healthcare investment. This investment is characterized as irreversible and occurs at a fixed continuous rate. A central aspect of the framework is the explicit modeling of health depreciation alongside aging and the direct link between health status and mortality risk. This dynamic interplay suggests that strategic healthcare investment can mitigate an individual's mortality risk.
Approach
The optimization problem is formulated as a stochastic control-stopping problem. Key state variables are the agent's wealth and health capital, operating within a random time horizon. To address this, the problem is transformed into its dual version, which manifests as a two-dimensional optimal stopping problem with interconnected dynamics. The analysis involves deriving the regularity of the optimal stopping value function. The related free boundary is characterized through a nonlinear integral equation, which is subsequently computed numerically. This computational step allows for a concrete determination of the conditions under which healthcare investment is optimal.
Findings
The framework indicates that an agent's decision to invest in healthcare is contingent upon their wealth exceeding a specific threshold. This threshold is defined by a health-dependent transformed version of the optimal stopping boundary. Numerical illustrations provided within the study depict these optimal strategies. The research also discusses certain financial implications arising from these optimal decisions.
Potential Applications
While the source does not explicitly detail applications, the framework models the joint determination of optimal consumption, portfolio choice, and irreversible healthcare investment, where health depreciates with age and affects mortality, and healthcare investment reduces mortality risk.
Key Limitations Mentioned by Researchers
No specific limitations are explicitly discussed by the researchers in the provided abstract.