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Questions about actuaries and mathematics!
Applied mathematics, of course. Applied mathematics includes

Nonlinear hyperbolic conservation law

Nonlinear elliptic equation

Numerical method of differential equation and its application

Mathematical physics

Inverse problem and its application

These are very basic and commonly used methods in actuarial science.

If you are engaged in research, you should apply mathematics better and broaden your horizons. Of course, finance is also a good choice. I don't think it is necessary to major in computational mathematics.