Precautionary risk reduction and saving : Two sides of the same coin?

We compile, generalize and extend the results about the comparative static effects of risk changes on optimal risk-reduction and saving behavior. We use the time-separable discounted expected-utility model and consider income risk, inflation risk, and interest rate risk. For each type of risk, we trace precautionary risk reduction and precautionary saving to the individual’s underlying risk apportionment preference. Risk reduction and saving are shown to be Edgeworth-Pareto substitutes for (mixed) risk-averters and Edgeworth-Pareto complements for (mixed) risk-lovers. This introduces feedback effects, and we identify conditions for jointly optimal risk-reduction and saving decisions to be Nth-degree risk substitutes or Nth-degree risk complements for the different types of risks