This paper develops a unified explicit solution theory for optimal execution through sequential limit-order placement in a limit order book. Rather than controlling only the trading speed of a metaorder, we determine how individual limit orders should be quoted over time. The model incorporates signal-dependent drift, price impact, inventory risk, and execution risk, with fills modeled by point processes whose intensities depend on the submitted quotes. We formulate four execution criteria: expected terminal wealth, expected terminal wealth with running inventory penalty, CARA utility of terminal wealth, and CARA utility with running inventory penalty. For general price-impact and inventory-penalty functions, we derive the corresponding HJB equations and show that all four problems reduce to a triangular finite-dimensional structure which can be solved explicitly, leading to fully explicit value functions and optimal quotes across all cases. We also prove well-posedness, admissibility, and verification results. The explicit formulas reveal connections between quoting strategies under different criteria, support long-horizon asymptotic analysis, and show numerically that signal-dependent drift can substantially affect optimal execution.

We study risk-neutral density extraction from short-dated option chains. As expiry approaches, option premia decline and bid--ask spreads can be large relative to prices, making mid quotes particularly uninformative. Stale or asynchronous quotes may also generate potential static arbitrages, rendering standard procedures infeasible or unstable. We develop a model-free pipeline that treats bid-ask quotes as the primitive market constraint. The pipeline consists of two steps. First, a procedure called ``Arbitrage Removal Iterative Executable Strategy'' (ARIES) filters executable static arbitrage at quoted bid and ask prices under market-depth constraints. Second, the ``Smooth Entropic Density EXtraction'' (SEDEx) then recovers the density through a criterion leveraging smoothness and entropy under bid-ask constraints. We test the pipeline on synthetic Heston panels and short-dated SPX option data, sampled from a few hours to one week before expiry. Computation is fast and returns robust densities across various market conditions, including scheduled macroeconomic announcements. As an empirical application, we use the recovered densities to construct short dated implied-volatility smiles.

The excess growth rate, defined as the gap in Jensen's inequality for the logarithm, is a fundamental functional in portfolio theory. In this paper, we present a mathematical study motivated by information theory. We begin by establishing its properties and showing that it has rich connections with information theoretic concepts such as the Helmholtz free energy, L. Campbell's measure of average code length and large deviations. Our main results consist of three axiomatic characterization theorems of the excess growth rate, in terms of (i) the relative entropy, (ii) the gap in Jensen's inequality, and (iii) the logarithmic divergence that generalizes the Bregman divergence. Furthermore, we study maximization of the excess growth rate and compare it with the growth optimal portfolio. Our results not only provide theoretical justifications of the significance of the excess growth rate, but also establish new connections between information theory and quantitative finance.

In this study, MLP models with dynamic structure are applied to factor models for asset pricing tasks. Concretely, the MLP pyramid model structure was employed on firm characteristic-sorted portfolio factors for modelling the large-cap US stocks. It was further developed as a practical factor investing strategy based on the predictions. The main findings were evaluated from 2 angles: model predictive power and backtesting performance, which were compared for the periods with and without COVID-19. The empirical results indicated that, given the constraints of the data size, the MLP models no longer perform 'deeper, better' in terms of predictive power, whereas the proposed MLP models with 2 and 3 hidden layers have greater flexibility in modelling the factors in this case. This study also verified the idea from previous work that MLP models for factor investing are more meaningful for downside risk control than for pursuing absolute annual returns.

The global momentum towards establishing sustainable energy systems has become increasingly prominent. Hydrogen, as a remarkable carbon-free and renewable energy carrier, has been endorsed by 39 countries at COP28 in the UAE, recognizing its essential role in global energy transition and industry decarbonization. Both the European Union (EU) and China are at the forefront of this shift, developing hydrogen strategies to enhance regional energy security and racing for carbon neutrality commitments by 2050 for the EU and 2060 for China. The wide applications of hydrogen across hard-to-abate sectors and the flexibility of decentralized production and storage offer customized solutions utilizing local resources in a self-paced manner. To unveil the trajectory of hydrogen development in China and the EU, this paper proposes a comparative analysis framework employing key factors to investigate hydrogen developments in both economic powerhouses. Beyond country-wise statistics, it dives into representative hydrogen economic areas in China (Inner Mongolia, Capital Economic Circle, Yangtze River Delta) and Europe (Delta Rhine Corridor) for understanding supply and demand, industrial synergy, and policy incentives for local hydrogen industries. The derived implications offer stakeholders an evolving hydrogen landscape across the Eurasian continent and insights for future policy developments facilitating the global green transition.