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The size effect that there exist return differences between small market-cap firms and large market-cap counterparts in the stock market has become one of the most controversial capital market anomalies. This paper aims to interpret this effect, including both the size premium and the size discount.

A dynamic capital mobility model (DCMM) is proposed, and the model’s explanatory ability is validated via simulation.

This study’s simulation results indicate that the observed size effect can be originated from the combination of the pure size effect and the investors’ herding behavior. Although the size premium, that average returns of small firms are higher than those of large firms, is more prevalent in the stock market, this study’s model implies that the size discount is also possible, which is largely an empirical issue. The pure size effect per se cannot reproduce the size premium. Only if the herding effect dominates the pure size effect would there exist the size premium.

Although the literature provides miscellaneous explanations for the size effect, they are still inconclusive. So far there has been no theory to directly investigate the size effect and to explicitly explore the impact of investors’ trading behavior on the size effect. To the best of the author’s knowledge, this paper fills in this gap and proposes a DCMM to interpret the size effect for the first time. In addition, while the literature focuses on the size premium only, this study covers not only the size premium but also the size discount.

Academia and financial practitioners have mixed opinions about whether artificial intelligence (AI) can beat the stock market. The purpose of this paper is to investigate theoretically what would happen if AI has further evolved into a superior ability to predict the future more accurately than average investors.

A theoretical model in an endowment economy with two types of representative investors (traditional investors and AI investors) is proposed, and based on the model, a long-run survival analysis for both types of investors is implemented.

The model presented in this paper indicates that being equipped with a superior ability to predict the future more accurately than traditional investors cannot guarantee AI investors to always beat the stock market in the long run. Those investors may be extinct, all depending on the structure/parameters of the stock market.

To the best of the author’s knowledge, they are the first to set up a representative agent equilibrium model to explore the above question seriously.

This paper aims to explore the allocation of the exit value of a start-up company in market equilibrium between an angel investor and an entrepreneur in the very early-stage financing market.

The theoretical model is established based on the two-sided random search theory and the model’s ability to match the empirical data is evaluated via simulation.

The model indicates that the allocation of the final investment outcome is not proportional to the initial investments by the angel investor and the entrepreneur. The simulation results show that the continued investment by the entrepreneur and the private benefit acquired by the angel investor have a more profoundly negative influence on the angel investor’s share of the exit value of the start-up company. Moreover, the market search structure represented by the matching probability of an angel investor to an entrepreneur has a more significant impact on the angel investor’s share than the other model parameters.

The importance of market search friction in the very early-stage financing market is emphasized. The concepts of continued investments and private benefits are introduced and quantified for the first time under the framework of angel investment. The impacts of such model parameters as the matching probability of an angel investor to an entrepreneur, the success rate of a start-up company, the bargaining power of an angel investor and the discount rate on the allocation of the exit value of the start-up company are investigated as well.