"having already studied" is correct and usable in written English.
You can use it to indicate that something has already happened before the current moment in time. For example: "Having already studied for the test, I was feeling confident about my chances of success."
Having already studied hypnosis, she now decides to take a course in writing, only to encounter more problems.
We were both still studying but, having already studied economics at A-level, the first year was a bit of a breeze.
At the time, MacKinnon, the bright daughter of a Republican congressman from Minnesota, was working on her PhD in political science at Yale, having already studied at Yale's Law School.
Another, though even less likely, shocker would be Mr. Clinton, who, having already studied the legal angles exhaustively, told CNN the other day that "a reasonable reading" of the 22nd Amendment is that "a former president can't run for vice president -- so I don't think that will happen".
Aim of experiment: Having already studied the effect of vertical load (Nagasao et al., 2002), the purpose of this study was to investigate the effect of horizontal load on implants embedded into a virtually reconstructed mandible.
He was encouraged to compete for a demyship to Magdalen College, Oxford – which he won easily, having already studied Greek for over nine years.
Vasilevsky replied, saying that Stalin had already studied this problem.
The bar association, which has already studied six other states' systems, offers solid suggestions for reform.
Like Coe, she had already studied the food of poverty, what people ate when they didn't have enough.
Ms. Marlowe said the book should carry a disclaimer: Anyone reading it should have already studied slavery.
June's face — the face I have already studied in photographs — is long and narrow and fine.
