论文标题
崩溃为平均值的法律不变功能
Law-invariant functionals that collapse to the mean
论文作者
论文摘要
我们讨论法律不变的凸功能何时“崩溃为平均值”。更确切地说，我们表明，在随机变量的大量空间中，在轻度的半内接种假设下，期望功能是仿射转化，是唯一沿着非恒定随机变量（非零期望）线性的唯一法律不变的凸函数。这扩展了文献中在有限的设置和对功能的其他假设下获得的结果。我们说明了我们一般结果对定价规则和风险措施的影响。
We discuss when law-invariant convex functionals "collapse to the mean". More precisely, we show that, in a large class of spaces of random variables and under mild semicontinuity assumptions, the expectation functional is, up to an affine transformation, the only law-invariant convex functional that is linear along the direction of a nonconstant random variable with nonzero expectation. This extends results obtained in the literature in a bounded setting and under additional assumptions on the functionals. We illustrate the implications of our general results for pricing rules and risk measures.
