Investment in health when health is stochastic

This paper applies stochastic control theory to the Grossman model of investment in health to characterize the case of a serious illness, i.e., one that permanently reduces the individual's stock of health capital. Health itself is modelled as a stochastic variable, whose variation over time is determined partly by a deterministic factor and partly by a random factor with a Poisson distribution. After setting out the equations for the deterministic and stochastic approaches, phase diagrams illustrate how the introduction of uncertainty alters the model. The framework is also used to consider the effect of the introduction of a vaccine.