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This paper describes how limited liability leads to risk-loving behaviour of nuclear power companies and on average too unsafe nuclear power plants. By reviewing current regulatory regimes, we show that this issue is not sufficiently taken care of by today's regulation. Therefore, we evaluate five regulatory instruments: (1) safety regulation, (2) minimum equity requirements, (3) mandatory insurance, (4) risk-sharing pools, and (5) catastrophe bonds. We conclude that none of these instruments in its pure form is recommendable. Thus, we propose a new approach that in its core consists of a two-stage procedure. On the first stage, capital markets assess the risk stemming from each nuclear power plant via catastrophe bonds. In the second step, the regulator uses this private risk assessment and intervenes by charging an actuarial fair premium in the sense of a Pigouvian risk fee. Society eventually acts as an explicit insurer for nuclear risk and is on average fairly compensated for the risk it is taking over.