Economic consequences of Nth-degree risk increases and Nth-degree risk attitudes

We study comparative statics of Nth-degree risk increases within a large class of problems that involve bidimensional payoffs and additive or multiplicative risks. We establish necessary and sufficient conditions for unambiguous impact of Nth-degree risk increases on optimal decision making. We develop a simple and intuitive approach to interpret these conditions : novel notions of directional Nth-degree risk aversion that are characterized via preferences over lotteries.