Carbon trading is a market-based mechanism for reducing greenhouse gas emissions, providing economic incentives for mitigating climate change and promoting the development of a low-carbon economy. However, China’s carbon market is still in its early stages of development, leading to limited data availability for deep neural network modeling. Consequently, accurately predicting price volatility in China’s carbon market is a challenging task. To address this issue, we propose a transfer learning framework based on the hybrid GARCH-GRU model, called CTr²L, to predict carbon price volatility. The CTr²L framework achieves comparable prediction accuracy to ordinary deep learning but with a significant reduction in required training data, and the effectiveness of CTr²L is verified through the ablation study. Furthermore, we propose a metric factor of the transferability of CTr²L, enabling us to verify the effectiveness of CTr²L before actual modeling and provide relevant guidance for time series data selection of source domains. Finally, we present the empirical results based on actual data to demonstrate the superiority of the proposed transfer learning framework in predicting carbon price volatility as well as the effectiveness of the proposed metric factor of the transferability.

The purpose of this paper is to investigate an optimal excess-of-loss reinsurance contract and investment problem involving two mutually cooperative insurers and a reinsurer, within the framework of the Stackelberg game. In the reinsurance contract, the two insurers are permitted to purchase excess-of-loss reinsurance from the reinsurer, who sets the pricing level for the reinsurance. Assume that the two insurers and the reinsurer invest their surpluses in a financial market comprising a risk-free asset and a risky asset, whose price process is described by geometric Brownian motion. Under the criterion of maximizing the expected exponential utility of their terminalwealth, the explicit expressions for the optimal strategies and the corresponding value functions are derived using techniques from optimal control theory and the dynamic programming method. Moreover, to further enhance the research system of reinsurance contract problems within the Stackelberg game framework, we also consider the optimization problem under the proportional reinsurance model. Finally,we present theoretical analyses and numerical examples to illustrate the economic intuition and insights gained from our results. An interesting finding is that the forms of the optimal proportional reinsurance strategy and the optimal excess-of-loss reinsurance strategy are remarkably similar, with differences primarily stemming from the type of reinsurance chosen by the insurers. In addition, we also discover that the two cooperating insurers will develop their own optimal reinsurance strategies based on their respective importance within the cooperative group.

Optimizing age-friendly community facilities has become crucial for enhancing elderly well-being. This study proposes a distributionally robust optimization (DRO) framework for public seating facility planning, addressing the limitations of conventional models in handling multidimensional uncertainties. We construct Wasserstein metric-based ambiguity sets to characterize stochastic interactions among individual physiological traits (e.g., balance capacity), environmental factors (e.g., terrain irregularity), and fatigue-induced risk accumulation. A dual-layer constraint system synergizes safety assurance (fall probability control) and functional adequacy (demand-responsive coverage) under budget limits. To address computational challenges in large-scale networks, we develop a Two-stage Greedy-deterministic (TSGD) algorithm with dynamic candidate screening and dual-variable correction, achieving high computational efficiency and scalability for large-scale networks. For small-scale validation, we further propose a Distributionally Robust Simulated Annealing (DRSA) algorithm. Numerical experiments demonstrate the following facts: 1) TSGD reduces computation time by 66% compared to Gurobi in 200-node scenarios with < 3% optimality gap; 2) The Wasserstein-DRO formulation ensures 89.3% risk compliance under worst-case uncertainty. Theoretically, this work integrates safety-functionality synergy into stochastic facility location models. Practically, it provides a decision-making paradigm for spatial optimization in aging communities, with algorithmic innovations enabling scalable implementation.

The dairy industry relies heavily on efficient milk manufacturing units to produce high-quality dairy products. Any disruption in the milk manufacturing process can have significant repercussions, including product contamination, financial losses, and potential danger to consumers. Therefore, ensuring the safety and reliability of the milk manufacturing system is paramount. In addition, failure probability analysis of components is essential for determining the most important preventive and corrective actions and identifying potential hazards. Many studies have implemented various techniques in traditional and fuzzy fault trees to perform detailed system reliability analyses. This study introduces a novel reliability analysis approach by incorporating the concept of a fault tree within an intuitionistic fuzzy framework. In this approach, triangular intuitionistic fuzzy numbers are utilized to accurately assess the failure potential of fundamental events in a milk processing unit. The study further applies approximate intuitionistic fuzzy arithmetic operations based on the weakest t-norm to improve the reliability of milk manufacturing systems. By incorporating the proposed approach, the failure probability of the milk manufacturing unit is obtained as (0.01132, 0.01142, 0.01227, 0.01537, 0.01547), with corresponding reliability values of (0.98677, 0.98688, 0.98773, 0.99083, 0.99093). This approach not only provides these estimates but also quantitatively evaluates the extent to which each basic failure event contributes to the overall system failure. The effectiveness of the aforesaid approach is further demonstrated through a systematic comparison of the obtained results with those from existing reliability assessment approaches.

Excessive workloads have a negative impact on healthcare quality. However, hospitalizations exhibit a varying distribution throughout the week, with a peak on Mondays and a decrease on weekends. This imbalance creates disparities for patients to have the same medical services level during peak times compared to non-peak times. So, we propose a dynamic programming model to minimize variance in daily service amounts by optimizing the number of admissions to smooth hospitalization demand and prevent overloads. Furthermore, we limit the maximum waiting size and service capacity to ensure system efficiency. However, the exponential growth of the state space with varying lengths of patient stays makes it challenging for traditional dynamic programming solutions. Therefore, we introduce a multi-agent constrained QMIX (C-QMIX) reinforcement learning algorithm to deal with complex states and get a stable solution. Finally, 81 weeks of data from a tertiary hospital in western China are used to test the algorithm. The results indicate a maximum reduction of 14% in variance while maintaining reasonable levels of average waiting time and overall service quantity and reducing the excessive occupancy rate to mitigate medical risks and enhance healthcare quality.