their

They used as an indefinite subject (sense 2) is sometimes objected to on the grounds that it does not have an antecedent. Not every pronoun requires an antecedent, however. The indefinite they is used in all varieties of contexts and is standard.

They, their, them, themselves: English lacks a common-gender third person singular pronoun that can be used to refer to indefinite pronouns (as everyone, anyone, someone). Writers and speakers have supplied this lack by using the plural pronouns <and every one to rest themselves betake — Shakespeare> <I would have everybody marry if they can do it properly — Jane Austen> <it is too hideous for anyone in their senses to buy — W. H. Auden>. The plural pronouns have also been put to use as pronouns of indefinite number to refer to singular nouns that stand for many persons <'tis meet that some more audience than a mother, since nature makes them partial, should o'erhear the speech — Shakespeare> <a person can't help their birth — W. M. Thackeray> <no man goes to battle to be killed. — But they do get killed — G. B. Shaw>. The use of they, their, them, and themselves as pronouns of indefinite gender and indefinite number is well established in speech and writing, even in literary and formal contexts. This gives you the option of using the plural pronouns where you think they sound best, and of using the singular pronouns (as he, she, he or she, and their inflected forms) where you think they sound best.