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This paper studies precautionary saving when many small risks are considered. We first introduce two simultaneous risks: labor income and interest rate risks. We show that, in this context, sufficient conditions for precautionary saving are weaker than in similar models. Moreover, we find that, unlike previous literature, precautionary saving can occur in the case of negative covariance between the two risks and in the case of imprudence. We then extend our analysis to a three-risk framework, where a background risk is included. We derive sufficient conditions for precautionary saving which are interpreted in the light of the previous literature.

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