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 notation.

中文翻译：

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固定收益市场中非凸成本和模型独立性的弱传输

我们考虑固定收益市场中与模型无关的定价问题，并表明它会导致 Gozlan 等人引入的弱最优运输问题。我们使用它来描述即期利率 Caplets 定价的极值模型，并建立第一个适用于固定收益市场的强大的超级复制结果。值得注意的是，弱传输问题表现出一个非凸的成本函数，因此没有被理论的标准假设所涵盖。在一个独立的部分，我们确定一般成本的弱输运问题可以简化为满足凸性假设的等价问题，从而扩展了弱输运理论的范围。这部分可能是它自己的利益，独立于我们的财务应用，