possessive pronoun

I´d like you to show me any mistakes there might be in this sentence, especially in relation to the use of the possessive pronoun:

"Joe and Lara remained together for 3 years although everybody used to tell them they were losing their youth by having such a steady relationship. However they said that they didn´t care, as the life and the problem were theirs."

[RonBee]

It is perhaps an unusual use of the word life, but I see nothing wrong grammatically with that sentence.

:)

[Tdol]

It would sound more natural if you said 'as it was their life and their problem'.