非凸偏好市场中的最优风险分配
Optimal risk allocation in a market with non-convex preferences
摘要：
本研究的目的有两个。首先，我们考虑一个非凸偏好的最优风险分配问题。通过建立失真风险测度的下确界表示，给出了最优和渐近最优配置存在的充要条件。我们将证明，类似于凸偏好的市场，在一个非凸框架中，失真风险度量的最优风险分配问题的有界性仅取决于偏好。其次，我们考虑相同的最优分配问题，通过增加进一步的假设，分配是共单调的。我们刻画了共单调最优风险分配，证明了“边际风险分配”只取0或1。值得注意的是，我们可以将市场偏好和总风险的作用分开。
英文摘要：
The aims of this study are twofold. First, we consider an optimal risk allocation problem with non-convex preferences. By establishing an infimal representation for distortion risk measures, we give some necessary and sufficient conditions for the existence of optimal and asymptotic optimal allocations. We will show that, similar to a market with convex preferences, in a non-convex framework with distortion risk measures the boundedness of the optimal risk allocation problem depends only on the preferences. Second, we consider the same optimal allocation problem by adding a further assumption that allocations are co-monotone. We characterize the co-monotone optimal risk allocations within which we prove the "marginal risk allocations" take only the values zero or one. Remarkably, we can separate the role of the market preferences and the total risk in our representation.
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