@article{discovery10189728, note = {Copyright {\copyright} The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust. This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (https://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.}, month = {February}, publisher = {Applied Probability Trust}, year = {2024}, title = {On some semi-parametric estimates for European option prices}, journal = {Journal of Applied Probability}, keywords = {Probabilistic inequalities; bounds for option prices;}, issn = {0021-9002}, author = {Marinelli, Carlo}, url = {https://doi.org/10.1017/jpr.2023.94}, abstract = {We show that an estimate by de la Pe{\~n}a, Ibragimov, and Jordan for E(X ? c){$^+$}, with c a constant and X a random variable of which the mean, the variance, and P(X ? c) are known, implies an estimate by Scarf on the infimum of E(X {$\wedge$} c) over the set of positive random variables X with fixed mean and variance. This also shows, as a consequence, that the former estimate implies an estimate by Lo on European option prices.} }