Let xn be a martingale with supnexn lt infin show that

Question

Problem:

Let (X_n) be a martingale with sup_nE|X_n| < ∞. Show that there  is a representation X_n  = Y_n - Z_n where (Y_n) and (Z_n) are non-negative martingales such that supn EY_n < ∞ and sup_n EZ_n < ∞

Additional Information:

This problem is basically from Mathematics as well as it is about non-negative martingale calculation