  Aggregating risks from multiple sources can be complex and demanding, and
decision makers usually adopt heuristics to simplify the decision process. This
paper axiomatizes two such heuristics, narrow bracketing and correlation
neglect, by relaxing the standard independence axiom in the expected utility
benchmark. Our representation theorem allows for either narrow bracketing, or
correlation neglect, or both of them. The flexibility of our framework allows
for applications in various setups. For example, we accommodate the
experimental evidence in narrow bracketing and risk aversion over small gambles
with background risk. In intertemporal choices, we show how our framework
unifies three seemingly distinct models in the literature and introduce a new
model that can satisfy many desirable normative properties in time preferences
simultaneously, including indifference to temporal resolution of uncertainty,
dynamic consistency and separation of time and risk preferences. One special
class of the model shares the same predictions as Epstein and Zin (1989) in
macroeconomics and finance applications, and is immune to the critique in
Epstein, Farhi, and Strzalecki (2014).
