Christmas message

In lieu of a Christmas bonus the chairman of the company that employs JD and I has boosted staff morale with an inspirational e-mail including the news that:

Each of our divisions has performed well and ahead of their respective markets

The word "respective" is meaningless in this context, but what about a spot of verb agreement? He could have written "Each of our divisions has performed well and ahead of its market" or "All of our divisions have performed well and ahead of their markets".

A minor point? Certainly – but we are a publishing house, after all.