The digital economy can change the proportions and types of production factors, gradually replace traditional backward production factors, reconstruct the division of labor and cooperation system, and improve productivity, which is an important basis for balanced and sufficient development. This paper measures the comprehensive level of the digital economy and balanced and sufficient development, by using Chinese provincial panel data from 2013 to 2021, and uses the panel fixed effect model, mediation effect model, and spatial econometric model to examine the digital economy’s effect on balanced and sufficient development as well as the digital economy’s mechanism. The results show that the digital economy has significantly promoted balanced and sufficient development, though there are obvious regional heterogeneity and spatial spillover effects, and the relevant conclusions are still valid after an endogenous treatment and a robustness test. The total factor productivity is an important mechanism for the digital economy to affect balanced and sufficient development.

With the development of deep submergence technology, submarine is widely used in many aspects as marine analysis and detection of marine resources. For the reason of strong nonlinearity and coupling in submarine exercise, it is difficult to get satisfactory control effect by conventional control method. In order to control objective of stable straight-line suspension underwater, how to control the change of rudder angle to stabilize attitude and improve the control performance is researched from feature analysis to submarine. Aiming at improving the global stability, kinetic character of straight-line suspension movement underwater is analyzed and modeled firstly, and model of nonlinear relationship about change of rudder angle and attitude is built then. Based on the conditions of global stability asymptotically of submarine tracking control underwater and the physical significance of tracking control by nonlinear proportion differential, a controller is designed for controlling horizontal rudder angle and vertical rudder angle by dynamic feedback, which achieve the balance of tracking controlling both in local and global and guarantee global stable convergence asymptotically. At last, the stability, effectiveness, and global convergence of controller are proved by the simulation experiment.

The option butterfly portfolio is the commonly option arbitrage strategy. In reality, because the distribution of the option state price density (SPD) function is not normal and unknown, so the nonparametric deep learning methods to estimate option butterfly portfolio returns are proposed. This paper constructs the single-index nonparametric option pricing model which contains multiple influencing factors and presents the nonparametric estimation form for option butterfly portfolio returns. The empirical analysis shows that the SPD function estimated by using single-index nonparametric option model can effectively calculate the option butterfly portfolio returns with the minimum option strike price interval and provide an effective reference tool for risk-averse investors with limited risk preferences.

The Latent Dirichlet Allocation (LDA) model is used to extract the text themes of newspaper news and construct the Chinese Economic Policy Uncertainty (EPU) Index. On this basis, based on the relevant data of Chinese A-share listed companies from 2008 to 2020, this paper empirically analyzes the impact of EPU on peer effects of firms R&D investment, and finds that EPU will aggravate the peer effects of firms R&D investment. Furthermore, the moderating effect of manager’s motivation to maintain reputation on the process of EPU influencing the peer effects of firms R&D investment was tested, and the mechanism of EPU influencing the peer effects of firms R&D investment through financial frictions was verified.