This paper studies the effects of an increase in risk on welfare and optimal policies in a stochastic dynamic model of global pollution. In a first step, we focus on the case of a single decision maker, and make use of an approach pioneered by Kimball (2014) for studying the impact of a marginal change in risk in optimal stochastic control models. Using a simple model with only one state variable and one control variable, we show how the optimal carbon tax responds to an increase in risk. It is found that the third derivative of the decay function of the stock of pollution may play a decisive role. In a second step, we investigate the extent to which Kimball's approach may be extended to the case of stochastic dynamic games. We show how strategic interactions complicate the task of evaluating the effects of an increase in risk. Interestingly, in a dynamic model of the tragedy of the commons, we find that an increase in risk can increase welfare even though all agents are risk averse. The reason is that higher risk can cause agents to be more conservative, and this mitigates the tragedy of the commons.