I always enjoy reading anything Isaac Ehrlich writes. In an NBER Working Paper with Yong Yin, he models the decision to buy health insurance. Since health insurance regulations prevent risk from being priced accurately, it turns out that self-insuring or relying on free care from safety note institutions is often optimal:
Our calibrated simulations  indicate that self-insurance and self-protection account for 31.3% of the uninsured by the baseline model, or 28.2% by the extended model. Jointly with the safety net system, these alternatives account for 50.3% and 45.5% of the uninsured, respectively. [...]
HT: Austin Frakt.