There aren't any rules against it.
However, that doesn't mean that your company profile can go around posting links to your website/product in all your answers: the rules outlined in the help article on How not to be a spammer still apply. This means that you shouldn't link to your company website unless if it contributes to the answer, your affiliation is disclosed and a summary of the contents of the link is presented in the answer so that people don't have to visit your site to find the actual answer.
If you're afraid that these companies will have their SEO boosted by posting on Mathoverflow, don't worry. All links generated by users on the SE network are
nofollowed, meaning that search engine bots won't follow links to their website. Note that this restriction is lifted once you reach 2000 rep, when any links to the URL in your profile are un-