发表机构
Kspectra Research Inc.（Kspectra研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文精确刻画了计价单位变更重加权的Wasserstein稳定性条件，指出一阶近似下计价单位抵消，唯一障碍是计价单位消失处的收益质量，并应用于传输文献中的矩假设。
AI 中文摘要
通过一个正的计价单位对概率律进行重加权，并将收益与计价单位之比向前推，得到计价单位变更重加权：年金测度下的互换利率律、鞅最优传输的计价单位对合反演，以及自归一化重要性抽样的总体形式。我们精确刻画了它何时是 Wasserstein 稳定的。在弱收敛输入、一致可积的计价单位以及严格正的极限计价单位均值下，重加权律的收敛等价于一个在输入下计算的、关于收益和计价单位的一个显式族的一致可积性条件。在一阶近似下，计价单位抵消，唯一障碍是计价单位消失处的收益质量；在缺乏这种质量的情况下，价格和一阶矩在仅有一致可积收益的条件下传递到极限，无需对倒数计价单位作任何假设。具有有界输入的两原子例子精确达到该阈值。应用刻画了传输文献中的一个常设矩假设，并界定了哪些年金测度统计量得以保留。
英文摘要
Reweighting a probability law by a positive numéraire and pushing forward the payoff-to-numéraire ratio yields the change-of-numéraire reweighting: the swap-rate law under the annuity measure, the numéraire-inversion involution of martingale optimal transport, and the population form of self-normalized importance sampling. We characterize exactly when it is Wasserstein-stable. Along weakly convergent inputs with uniformly integrable numéraires and a strictly positive limiting numéraire mean, convergence of the reweighted laws is equivalent to a uniform integrability condition, computed under the inputs, on one explicit family in the payoff and numéraire. At first order the numéraire cancels, the sole obstruction being payoff mass where the numéraire vanishes; absent such mass, prices and first moments pass to the limit under a uniformly integrable payoff alone, with no assumption on the reciprocal numéraire. Two-atom examples with bounded inputs attain the threshold exactly. Applications characterize a standing moment assumption in the transport literature and delimit which annuity-measure statistics survive.
Comments16 pages. Also on SSRN as abstract 7383120: https://ssrn.com/abstract=7383120
