I am currently an international student doing a PhD in mathematics (Top 50 program) in the US. I just finished my first year. Having passed my qualifying exams, I now have to start thinking about my comprehensive exam. Now the problem is, the only person active in the area (financial maths) I'm interested in will be retiring soon and is no longer accepting students.
After some thorough search I have found a couple of programs (financial engineering PhD) that are highly competitive but perfectly fit my interests. My plan is to apply to these programs and leave my current program with a Masters in case I get admitted into one of them.
Now here are my questions:
Is this an acceptable thing to do?
Should I tell my potential advisors in my current program about my plan? I'm actually thinking of asking one of them for a reference letter for my application.
Are my chances of getting into a new PhD program affected in anyway by the fact that I currently in another PhD program?