What is the ruling on Umrah and Hajj for a woman whose father has died and who does not have a mahram to travel with her?

The detailed discourse of the scholars regarding a woman's travel for Hajj or 'Umrah without a mahram has been previously elaborated. The preponderant opinion is the permissibility of her travel for both (Hajj and 'Umrah) without a mahram if she is able, travels with a trustworthy company, and is secure from encountering fitnah (temptation or tribulation).