In order to control non-equilibrium processes and to describe the fat-tail phenomenon in econophysics, we generalize the traditional the Fokker-Planck equation (FPE) by including a quadratic correlation potential, and by making the time-dependent drift-diffusion coefficients. We investigate the su(1, 1) ~ u(1) algebraic structure and obtain the exact solutions to the generalized time-dependent FPE by using the algebraic dynamical method. Based on the exact solution, an important issue in mode econophysics, i.e. the fat-tail distribution in stock markets, is analysed.