异质信念下基于 Lambda 风险价值的风险分担
Risk sharing with Lambda value at risk under heterogeneous beliefs
AI总结：
本文研究异质信念下多主体以 Lambda Value-at-Risk 为偏好的风险分担，给出下确界卷积与最优配置公式，并分析不同信念关系及双主体一般风险测度情形。
摘要：
本文研究多个主体在异质信念下以 Lambda Value-at-Risk（Lambda 风险价值）作为偏好泛函的风险分担问题，其中信念由若干概率测度表示。我们得到了异质信念下多个 Lambda Value-at-Risk 测度的下确界卷积的半显式公式，以及相应最优配置的显式形式。为展示信念异质性的影响，我们考虑三种情形：同质信念、条件信念和绝对连续信念。针对这些情形，我们得到了下确界卷积的更显式表达式，揭示了信念之间的关系对下确界卷积的影响。此外，在双主体设定下，我们考虑一个 Lambda Value-at-Risk 与一般风险测度在不同信念下的下确界卷积，该一般风险测度将期望效用、扭曲风险测度和 Lambda Value-at-Risk 作为特例，并得到了下确界卷积的表达式和最优配置的形式。在上述所有情形中，我们证明当信念不一致程度和风险容忍度均较高时会出现平凡结果。最后，我们讨论了 Lambda Value-at-Risk 的另一种定义下的风险分担。
英文摘要：
In this paper, we study the risk sharing problem among multiple agents using Lambda Value-at-Risk as their preference functional, under heterogeneous beliefs, where beliefs are represented by several probability measures. We obtain semi-explicit formulas for the inf-convolution of multiple Lambda Value-at-Risk measures under heterogeneous beliefs and the explicit forms of the corresponding optimal allocations. To show the impact of belief heterogeneity, we consider three cases: homogeneous beliefs, conditional beliefs and absolutely continuous beliefs. For those cases, we find more explicit expressions for the inf-convolution, showing the influence of the relation of the beliefs on the inf-convolution. Moreover, we consider, in a two-agent setting, the inf-convolution of one Lambda Value-at-Risk and a general risk measure, including expected utility, distortion risk measures and Lambda Value-at-Risk as special cases, with differing beliefs. The expression of the inf-convolution and the form of the optimal allocation are obtained. In all above cases we demonstrate that trivial outcomes arise when both belief inconsistency and risk tolerance are high. Finally, we discuss risk sharing for an alternative definition of Lambda Value-at-Risk.
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