There has been very little research to test whether ambiguity affects individuals' decisions to insure themselves against the catastrophic effects of climate change. This paper attempts to study how individuals respond to the availability of an insurance that would give them immunity to a climate change catastrophe. Moreover, if such an insurance is available to them, do they insure themselves sufficiently? Further, the study investigates the policy implications for insurance companies: does increased availability of information regarding the probability of the catastrophic event, lead to an increase in insurance subscriptions? Finally, policy implications for the State are investigated - Can State intervention ensure a better outcome?