Is it permissible for a woman to travel without a mahram if her parents consider it a necessity and insist upon it?

Scholars have unanimously agreed on the prohibition of a woman traveling without a mahram if there is a fear of fitna (temptation/strife). They differed, however, if there is no fear of fitna. Some of them prohibited it, acting on the generality of the hadiths, while others permitted it with a safe companion, this being the view of the Malikis and Shafi'is. Some scholars specified this permission only in cases of dire necessity.

As for a young woman, safety from fitna is hardly achievable in this era. Therefore, it is not permissible for you to travel without a mahram, because it is prohibited, and obedience to parents is not allowed in a matter of disobedience [to Allah].