This paper presents a proposal for a regulatory regime aimed at reducing systemic risk effectively and internationally. Systemic relevance should be internalized with a levy (or "tax"), the level of which (or "tax rate") rises with the systemic relevance of an institution (Pigouvian taxation). The levy should be complemented by a Systemic Risk Fund which is endowed with control rights, in particular early intervention and resolution powers. The Systemic Risk Fund should be funded by the proceeds from the levy; if the Fund reaches a certain threshold size, the continuing flow of contributions is distributed to the government(s). Systemic Risk Funds implemented on the global, European, and national level would solve the issue mitigating risks also cross-border and provide a framework for burden-sharing.