Transition from Finance to Applied mathematics Currently studying a Bsc in Accounting &amp; Finance. During my studies if found an increased interest on subject such as Stochastic calculus, measure theory and mathematical analysis. I want to pursue a Msc in Applied Mathematics but wondering whether the transition is possible. 

I would be pleased if someone could provide me certain similar cases/experiences or some advice with reference to study material.
As with any application, you need to make your case. But if you have studied those three math subjects and have a good understanding of them, I think you have a basis. It might be especially possible if your future studies apply math to the financial realm, of course. 

It would be harder to get into a program with admissions systems that mostly check boxes of requirements rather than looking at individuals. If the admissions process gives you access to professors and potential advisors it would be easier, provided that you can convince someone that you can manage the early courses that might be required.