A self-insurer will need to be assured that the company will still be in existence when claims need to be paid. In the USA, A.M. Best provides ratings for each insurance company with A+ being the highest category. If a self-insurer is unsure of a company's credentials they should obtain outside advice.
A self-insurer will need to be assured that the excess insurer responds quickly, efficiently and responsibly to any claims so that the company is not left having to fund them itself.
A self-insurer will need to be assured that an insurer's prices are not out of line with the market or excessively high. It may sometimes be appropriate for a broker or a Third Party Administrator to provide a company with alternative quotes at renewal, but unless there is a significant price differential (and all other things being equal) changing the excess insurer should be resisted. Stop-loss insurers normally take into account prior loss experience and add a discount if the insured has been a loyal customer. Moving to another insurer for a short-term gain can often turn out to be counter-productive in the long-term.
If experience is positive and a premium bank is developed, a self-insurer will want to be assured that the excess insurer will take this into account in calculating future premiums in order that the company will benefit from reduced premiums.
Also in this section
Initial Considerations for Self-Insuring Employee Benefit Trusts
Administering a Self-Insured Employee Benefits Trust
Appointing an Employee Benefit Trust Plan Administrator
How Self-Insured Employee Benefits Stop-Loss Insurance works
Self-Insured Employee Benefits In The USA - How The ERISA Act of 1974 Works