We investigate the economic impact of stochastic endogenous extreme events and insurance in a growth model. Our analytical results and computational experiments show that i) transparency of the insurance sector is the decisive requisite for abatement activities, implying substantial policy opportunities; ii) we can fully characterize and quantify the impact of uncertainty on the agent's decisions; iii) a decentralized economy will under-invest in abatement without adequate policy interventions; iv) precautionary beliefs on the frequency of extreme events lead to more sustainability; v) technical change does not change the ordering of the paths but leads to a more sustainable future; v) a social security system which prices insurance fairly is preferable to an insurance industry which provides insurance with an overhead