Praise be to Allah.
The basic principle with regard to jihaad is that it is fard kifaayah, i.e. if a sufficient number of people undertake this duty, then there is no sin on the rest of the community. If it is fard kifaayah, then the mujaahid is obliged to seek permission before going for jihaad. He has to seek his parents’ permission if they are Muslim, regardless of whether they are rich or not and regardless of whether they can do without his help or not, because the texts clearly state that he has to seek his parents’ permission. One such text was reported in al-Saheehayn from ‘Abd-Allaah ibn ‘Amr, who said that a man came to ask the Prophet (peace and blessings of Allaah be upon him) for permission to go for jihaad. He said, ‘Are your parents still alive?’ [The man said] ‘Yes.’ He said, ‘Then your jihaad is with them.’ Imaam Ahmad, Abu Dawood and Ibn Hibbaan narrated from Abu Sa’eed that the Messenger of Allaah (peace and blessings of Allaah be upon him) sent a man who had made hijrah from the Yemen back to his parents. He (the Prophet (peace and blessings of Allaah be upon him)) said, ‘Did they give you permission?’ [The man] said, ‘No.’ He said, ‘Go back to them and seek their permission, and if they give you permission, then go for jihaad, otherwise honour and respect them.’
The above applies in cases where jihaad has not become obligatory on every single person, i.e., fard ‘ayn. If jihaad becomes fard ‘ayn, then it is not obligatory to seek permission, because in the case of things which are fard ‘ayn, there is no need to seek the permission of anyone. Jihaad becomes fard ‘ayn when a person is in the battlefield, if the enemy invades a Muslim country, if the imaam appoints a person or urges him to fight, or if his particular skills are needed because he has good knowledge of military matters or weapons and so is needed by the mujaahideen, and there is no one else with this knowledge or these skills. And Allaah knows best.