Precautionary Saving against Correlation under Risk and Ambiguity ^a

Abstract This paper considers precautionary saving against the correlation between two risky attributes (wealth and health) and investigates how the correlation affects optimal savings under multivariate preferences. The signs of higher‐order cross‐derivatives play a key role in determining the direction of precautionary saving against such correlation. Mixed correlation‐averse (seeking) individuals increase (decrease) savings in response to increases in correlation. Furthermore, we introduce ambiguity to the correlation and investigate how ambiguity affects the amount of optimal savings. The analyses enable us to deepen our understanding of saving behavior under multivariate preferences in the presence of correlation.