AXA S.A is telling federal regulators that “life insurance companies are highly unlikely to pose a system risk to the U.S. financial system.”

AXA, the French parent of AXA Equitable Life Insurance Company, sent its remarks in a comment letter to the Financial Stability Oversight Council (FSOC). In an advance notice of proposed rulemaking, the Council is asking what criteria should be used in subjecting non-bank financial companies to heightened supervision by the Federal Reserve Board under Sec. 113 of the new Dodd-Frank law.

The provision authorizes the FSOC to determine if a U.S. or foreign nonbank financial company should be subject to Fed supervision under “heightened prudential standards.”

The provision calls for increased supervision if the FSOC finds “material financial distress” at the company “or the nature, scope, size, scale, concentration, interconnectedness, or mix of the activities” of a company “could pose a threat to the financial stability of the United States.”

The AXA letter states that no “single criterion should determine systemic risk, and systemic risk criteria generally do not fit life insurance companies.”

Moreover, the letter says, “insurance is a particularly vivid example of the need to avoid relying on size–for example, looking to an insurer’s total assets under management does not distinguish between proprietary assets and customer assets held in separate accounts,” citing a report by the International Association for the Study of Insurance Economics (IAIS).

The letter also notes comments in the IAIS report that “size has a beneficial effect for most insurers by allowing greater diversification of risk.”

The letter adds AXA “diversifies AXA Equitable’s exposure to the U.S. life insurance market through a worldwide group of companies active in life insurance, property and casualty insurance, asset management and other related businesses. We believe that this diversification helped protect AXA during the recent financial crisis and will continue to serve it well in the future.” the letter said.

The letter also said that asset managers such as its AllianceBernstein unit are highly unlikely to pose a systemic risk to the U.S. financial system and also contended that the FSOC should not take unilateral action with foreign financial companies.