On the risk-downside risk tradeoff

In the last decade the literature has established the empirical importance of the tradeoff between risk and downside risk in a variety of economic settings. While the notions of risk and downside risk have been generalized in the theoretical literature, the literature has yet to provide a choice-theoretic characterization of their tradeoff. This paper provides an analytical characterization of the risk-downside risk tradeoff and shows its relevance in the analysis of optimal decisions under uncertainty, such as the precautionary savings decision.