标题： 广义Orlicz保费 显示英文标题

标题： Generalized Orlicz premia

摘要： 我们引入了一个广义的Orlicz溢价版本，基于可能非凸的损失函数。 我们证明了这个广义定义涵盖了各种相关示例，例如几何平均数和期望值，同时保留了一些相关性质。 我们确立了现金可加性导致$L^p$-分位数，扩展了关于凸Orlicz溢价“坍缩到均值”的经典结果。 然后我们专注于几何凸的情况，讨论广义Orlicz溢价的对偶表示，并将其与凸情况的标准对偶表示的乘法形式进行比较。 最后，我们证明了广义Orlicz溢价自然地作为唯一可诱发、正齐次、单调且归一化的泛函出现。 显示英文摘要

摘要： We introduce a generalized version of Orlicz premia, based on possibly non-convex loss functions. We show that this generalized definition covers a variety of relevant examples, such as the geometric mean and the expectiles, while at the same time retaining a number of relevant properties. We establish that cash-additivity leads to $L^p$-quantiles, extending a classical result on 'collapse to the mean' for convex Orlicz premia. We then focus on the geometrically convex case, discussing the dual representation of generalized Orlicz premia and comparing it with a multiplicative form of the standard dual representation for the convex case. Finally, we show that generalized Orlicz premia arise naturally as the only elicitable, positively homogeneous, monotone and normalized functionals.