In recent years, bidirectional associative memory (BAM) neural networks have been extensively studied and applied to many different fields. Many researchers have studied in existence and uniqueness of solution, periodic oscillatory solution, global asymptotic or exponential stability of the equilibrium point. The time delays in a neural network may affect its dynamics. To the best of our knowledge, there are little of research results on anti-periodic solutions of the neural networks with multiple delays. This thesis will concern on a class of interval general BAM neural networks with multiple delays. For a special stochastic BAM neural networks, stochastic Hopfield neural networks with mixed delays are also considered. Effective numerical scheme for backward stochastic differential equations (BSDEs) is an important topic in theory of BSDEs. Therefore, a regression-based numerical scheme for BSDEs will be proposed. The first part of this thesis is devoted to the stabilities of some systems. First, some BAM neural networks with multiple delays will be introduced. In this part, some definitions and important known results have been given. Based on the fundamental solution matrix of coefficients, inequality technique and Lyapunov method, a series of sufficient conditions to ensure the existence and exponential stability of anti-periodic solutions of the neural networks with multiple delays are given. Next, BAM neural networks with external perturbations, that is stochastic BAM neural networks, will be introduced. A special of these systems-stochastic Hopfield neural networks with mixed delays are also considered. Employing Ità formula and applying the in equality techniques, two sufficient conditions ensuring almost surely exponential stability and pth moment exponential stability are proved, including mean square exponential stability. The main results derived in this part generalize the known results. Finally, some examples are chosen to illustrate the effectiveness. The second part of this thesis concerns with numerical solution of BSDEs. Since the theory of BSDEs has successfully applied in economics and finance for many years, how to get the numerical solution of BSDEs is an important problem. In short, a theory of BSDEs solves a boundary value problem for the evolution of a stochastic process, given a terminal condition for the process. First, some current research of BSDEs has been introduced. Next, in discretization of BSDEs, the classical Euler method to discretize the forward and backward SDEs are used. Combined with Feynman-Kac Theorem, some kinds of conditional expectations will be handled. Based on Fourier cosine expansion, two approximations of conditional expectations are studied, and the local errors for these approximations are analyzed. Using these approximations and the theta-time discretization, a new and efficient numerical scheme, which is based on least-squares regression, for forward-backward stochastic differential equations (FBSDEs) is proposed. Thirdly, numerical experiments are done to test the availability and stability of this new scheme for Black-Scholes call and calls combination under an empirical expression about volatility. Lastly, this new method will be applied to a wide of financial derivatives-pricing Bermudan callable bonds. Finally, we make conclusions of the thesis, and give some future research works.