A growth model with regime switch
Continuing on the comments exchange, the conclusion that the overall effect is to change the discount factor, is similar to the one reached in the original Overlapping Generations Model of Blanchard, where individuals are faced with a "probability of death" (surely a "catastrophic event" I believe).

See the Blanchard &amp; Fischer book "Lectures in Macroeconomics", p. 117. The authors note that the result has been originally obtained by Cass and Yaari (1967) "Individual Saving, Aggregate Capital Accumulation, and Efficient Growth", a paper that is part of the book Essays on The Theory of of Optimal Economic Growth