First-order (Conditional) Risk Aversion, Background Risk and Risk Diversification

In the literature, utility functions in the expected utility class are generically limited to second-order (conditional) risk aversion, while non-expected utility functions can exhibit either first-order or second-order (conditional) risk aversion. This paper extends the concepts of order of conditional risk aversion to orders of conditional dependent risk aversion. We show that first-order conditional dependent risk aversion is consistent with the framework of the expected utility hypothesis. We relate our results to risk diversification and provide additional insights into its application in different economic and finance examples.