Stability of Change-of-Numéraire Reweighting: An Exact Wasserstein Boundary
Abstract
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.
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BibTeX
@misc{huang2026stability,
title = {{Stability of Change-of-Numéraire Reweighting: An Exact Wasserstein Boundary}},
author = {Shaosai Huang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30329},
eprint = {2609.30329},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30329},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Stability of Change-of-Numéraire Reweighting: An Exact Wasserstein Boundary
AU - Shaosai Huang
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30329
UR - https://arxiv.org/abs/2609.30329
AB - 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.
ER -