Increasing Risk in the Presence of Correlated Background Risk

This work develops a partial ordering of risks in the presence of a correlated background risk, which is parallel to the structure of [Ekern, S (1980). Increasing [Formula: see text]th degree risk. Economic Letters, 6, 329–333]’s risk increase. We introduce the notion of truncation expectation dependence to measure the primary risk’s dependence on the background risk. We provide its integral characterization of distribution functions. Within a bivariate expected utility framework, we show an equivalence between the sign of cross-derivatives of the utility function with the preference toward truncation expectation dependence. This choice-theoretic foundation is helpful for studying some economic and financial decisions with background risks, e.g., optimal portfolio, precautionary effort.