According to many observers, the world is currently getting riskier along many of its dimensions. In this paper we analyse how the welfare state, i.e., social insurance that works through redistributive taxation, should deal with this trend. We distinguish between risks that can be insured by the welfare state and such than cannot (background risks). Insurable risks can be reduced either by individual self-insurance or, through pooling, by social insurance. Both ways are costly in terms of income foregone. We show: (i) Self-insurance will be higher the more costly is the welfare state and the larger are background or insured risks. (ii) Full risk coverage by the welfare state can only be optimal in a costless welfare state. (iii) The optimal size of the welfare state is larger the higher are the risks that it cannot insure. The impact of the size of risks that can be insured is, however, unclear.