This was part of Technological Innovation in Health Care Delivery
Consumption Decision, Portfolio Choice and Healthcare Irreversible Investment
Giorgio Ferrari, Universität Bielefeld
Wednesday, May 17, 2023
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 choice problem, where, in addition, the agent can choose the time at which undertaking a costly 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 original 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 optimal stopping 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. This is based on a joint work with Shihao Zhu (Bielefeld University).