Financial Risk Taking in the Presence of Correlated Non-Financial Background Risk

This paper characterizes the stochastic deterioration resulting from taking a zero-mean financial risk in the presence of correlated non-financial background risk. We show in particular that it has an equivalent stochastic order as well as a necessary and sufficient "integral condition'' that implies and is implied by a particular sense in which the stochastic deterioration can be decomposed into a "correlation increase'' and a "marginal risk increase''. We further characterize a measure of aversion to the stochastic deterioration. These characterizations provide for a more general framework for formulating concepts of increases in risk and correlation and for better understanding risk management decisions governed by individuals' attitudes to them.