Capital requirements of health insurers under different risk-adjusted capitation payments

Defining optimal capital requirements for health insurers is a matter of interest for policy-makers. They determine the insolvency probability of health insurers and the minimum number of enrolees in order to keep insolvency under control. In this paper we develop a methodology for estimating the expected loss per health insurer after considering their specific risk profile and the capitation formula with which they are paid. We assume the expected loss follows a normal distribution within risk pools consisting of a unique combination of long-term disease, age, gender, and location, and then define the minimum capital requirement as the 1st quantile of the loss distribution. An application is made for insurers in the statutory health care system of Colombia.