Decreasing Downside Risk Aversion and Background Risk

In this paper, we show that risk vulnerability can be associated with the concept of down- side risk aversion (DRA) and an assumption about its behavior, namely that it is decreas- ing in wealth. Specifically, decreasing downside risk aversion in the Arrow-Pratt and Ross senses are respectively necessary and sufficient for a zero-mean background risk to raise the aversion to other independent risks.