The Swiss Federal Office of Public Health inspects mandatory basic health insurance provided by each insurer and their financial assets: Inspection results for 2011
(Explanations can be found in this PDF document).
They make sure that outstanding costs in customers' favour can be paid. These also need re-insurance for expensive cases. All health insurance providers must contribute to a general security fund as stipulated by law. This enables costs to be paid in case a provider should not be able to cover his own.
For low premiums, an equal percentage of men, women and children and a low age average is important. According to the RVK, smaller and medium-sized providers have better customer profiles, which is why they must pay contributions to larger insurance providers with high-risk profiles.
If premiums rise or if the insurance providers stop operating, you will be able to switch insurers easily: Every insurer must accept you as a customer without reservation.