We study market efficiency in an infinite-horizon model with a monopolistic insider. The insider can trade with competitive market makers and noise traders, and observes privately the expected growth rate of asset dividends. In the absence of the insider, this information would be reflected in prices only after a long series of dividend observations. Thus, the insider's information is "long-lived." Surprisingly, however, the monopolistic insider chooses to reveal her information very quickly, within a time converging to zero as the market approaches continuous trading. Although the market converges to strong-form efficiency, the insider's profits do not converge to zero.2

We study market efficiency in an infinite-horizon model with a monopolistic insider. The insider can trade with a competitive market maker and noise traders, and observes privately the expected growth rate of asset dividends. In the absence of the insider, this information would be reflected in prices only after a long series of dividend observations. The insider chooses, however, to reveal the information very quickly, within a time converging to zero as the market approaches continuous trading. Although the market converges to strong-form efficiency, the insider's profits do not converge to zero.

We propose an approach to predict the natural gas price in several days using historical price data and events extracted from news headlines. Most previous methods treats price as an extrapolatable time series, those analyze the relation between prices and news either trim their price data correspondingly to a public news dataset, manually annotate headlines or use off-the-shelf tools. In comparison to off-theshelf tools, our event extraction method detects not only the occurrence of phenomena but also the changes in attribution and characteristics from public sources. Instead of using sentence embedding as a feature, we use every word of the extracted events, encode and organize them before feeding to the learning models. Empirical results show favorable results, in terms of prediction performance, money saved and scalability.

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This work proposes a Physics-informed Machine learning method to model and emulate the progression of COVID-19. Besides the high accuracy, lower data need, and interpretability, the method also estimates hidden parameters from data, which are useful for policymakers to flatten the curve and better understand public healthcare system.