Either one might be correct. In general, your would be more formal, but it depends how you use it in a sentence. Can you give examples using full sentences?
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It is a matter of emphasis: "your having" is usually preferable and in general more formal. I assume here that you are preceding an infinitive such as "to do." When using "your", however, the focus is on the act of having (to do) - for example: "without it being necessary that something be done." Using "you having" shifts the emphasis to "you": "without it being you, as opposed to another,