论文标题
在固定收入市场中非凸成本和模型独立的运输薄弱
Weak Transport for Non-Convex Costs and Model-independence in a Fixed-Income Market
论文作者
论文摘要
我们考虑了固定收益市场中与模型无关的定价问题，并表明它导致了Gozlan等人提出的薄弱最佳运输问题。我们使用它来表征以货率定价的极端模型，并建立一个适用于固定收益市场的首个强大的超级复制结果。 值得注意的是，弱运输问题表现出非凸的成本函数，因此该理论的标准假设不涵盖。在独立的部分中，我们确定一般成本的薄弱运输问题可以简化为确实满足凸度假设的等效问题，从而扩大了弱运输理论的范围。这部分可能与我们的财务应用无关，并且不熟悉数学金融符号的读者可以使用。
We consider a model-independent pricing problem in a fixed-income market and show that it leads to a weak optimal transport problem as introduced by Gozlan et al. We use this to characterize the extremal models for the pricing of caplets on the spot rate and to establish a first robust super-replication result that is applicable to fixed-income markets. Notably, the weak transport problem exhibits a cost function which is non-convex and thus not covered by the standard assumptions of the theory. In an independent section, we establish that weak transport problems for general costs can be reduced to equivalent problems that do satisfy the convexity assumption, extending the scope of weak transport theory. This part could be of its own interest independent of our financial application, and is accessible to readers who are not familiar with mathematical finance notations.
