Although the concept of entropy is originated from thermodynamics, its concepts and relevant principles, especially the principles of maximum entropy and minimum cross-entropy, have been extensively applied in finance. In this paper, we review the concepts and principles of entropy, as well as their applications in the field of finance, especially in portfolio selection and asset pricing. Furthermore, we review the effects of the applications of entropy and compare them with other traditional and new methods.

In this paper, we define the portfolio return as fuzzy average yield and risk as hybrid-entropy and variance to deal with the portfolio selection problem with both random uncertainty and fuzzy uncertainty, and propose a mean-variance hybrid-entropy model (MVHEM). A multi-objective genetic algorithm named Non-dominated Sorting Genetic Algorithm II (NSGA-II) is introduced to solve the model. We make empirical comparisons by using the data from the Shanghai and Shenzhen stock exchanges in China. The results show that the MVHEM generally performs better than the traditional portfolio selection models.

This paper attempts to evaluate the coordinated development state of the subsystems within the internet financial ecosystem in China from 2011 to 2016. Focusing on the main business modes, technological innovation, and the external environment, we select 29 indicators to construct an index system and adopt a coupling coordination degree model for evaluation. Furthermore, we use two weight calculation methods, entropy weight and principal component analysis, to ensure the robustness of the results. The empirical results show that China’s internet financial ecosystem experienced five development stages from 2011 to 2016, which are moderate disorder, near disorder, weak coordination, intermediate coordination, and good coordination. Different methods of obtaining weights have little effect on the empirical results. These findings suggest that at the beginning, the coordinated development of China’s internet financial ecosystem was hindered by factors including the scarcity of main business modes and the defect of technological innovation; then, with the rapid development of China’s internet industry, the external environment became another drawback in coordinated development. Finally, based on the findings, we give some policy recommendations from a global perspective to achieve a sustainable internet financial ecosystem.

This study investigates a firms financing, investment, and payout policies through a rational expectation equilibrium based on which managers and outside investors have heterogeneous prior beliefs. The proposed model demonstrates that managers tend to overinvest (underinvest) if the extent of heterogeneousness is above (below) a threshold, which differs under distinct circumstances. Moreover, a price bubble is positively related to overinvestment, and the model shows that a firms optimal financing choices and payout policies vary with the assumption of heterogeneous beliefs.