Optimal Transport for Actuarial Science
Abstract
These lecture notes introduce optimal transport as a mathematical language for actuarial science. They treat losses, premiums, scores, reserves, capital scenarios, climate losses and lifetime distributions as probability measures that can be compared, transported, averaged, stressed and interpolated. The first part develops the main tools: couplings, push-forwards, discrete and continuous Kantorovich problems, duality, Wasserstein distances, quantile transport, barycenters, entropic regularization and statistical optimal transport. The second part applies these tools to risk measures, Wasserstein robustness, pricing and capital, portfolio drift, reserving cash-flow distributions, climate-prevention diagnostics, reinsurance, dependence uncertainty, capital allocation, distributional fairness diagnostics and longevity risk. Later chapters and appendices discuss counterfactual transport, dynamic formulations, unbalanced transport, Schrödinger bridges, cost engineering and computational labs in R. The emphasis is on actuarial modelling choices: the state space, the ground cost, the ambiguity radius, the reference distribution and the interpretation of the transport plan. Transport maps and couplings are used as distributional objects, not as causal claims unless additional assumptions are imposed.
Related
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- Convergence of Coordinate Ascent Variational Inference for log-concave measures via optimal transport
- Resident Medical Insurance Contribution Schemes and Fiscal Burden in China: An Actuarial Projection Under Demographic Dynamics
- Method of successive approximations for solving integral equations of actuarial mathematics
- Hausdorff dimension of the singular set in optimal transport
BibTeX
@misc{charpentier2026optimal,
title = {{Optimal Transport for Actuarial Science}},
author = {Arthur Charpentier},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08797},
eprint = {2610.08797},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08797},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Optimal Transport for Actuarial Science
AU - Arthur Charpentier
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.08797
UR - https://arxiv.org/abs/2610.08797
AB - These lecture notes introduce optimal transport as a mathematical language for actuarial science. They treat losses, premiums, scores, reserves, capital scenarios, climate losses and lifetime distributions as probability measures that can be compared, transported, averaged, stressed and interpolated. The first part develops the main tools: couplings, push-forwards, discrete and continuous Kantorovich problems, duality, Wasserstein distances, quantile transport, barycenters, entropic regularization and statistical optimal transport. The second part applies these tools to risk measures, Wasserstein robustness, pricing and capital, portfolio drift, reserving cash-flow distributions, climate-prevention diagnostics, reinsurance, dependence uncertainty, capital allocation, distributional fairness diagnostics and longevity risk. Later chapters and appendices discuss counterfactual transport, dynamic formulations, unbalanced transport, Schrödinger bridges, cost engineering and computational labs in R. The emphasis is on actuarial modelling choices: the state space, the ground cost, the ambiguity radius, the reference distribution and the interpretation of the transport plan. Transport maps and couplings are used as distributional objects, not as causal claims unless additional assumptions are imposed.
ER -