Is it permissible for a wife to observe a supererogatory fast without her husband's permission, and if she refuses and fasts, is her fast valid, and is she sinful?

It is not permissible for a woman to observe a supererogatory fast in the presence of her husband except with his permission. If a woman fasts without her husband's permission, she incurs sin for disobeying the prohibition of the Prophet (peace be upon him) and the command of her husband. However, her fast is valid according to the majority of jurists.