Rapidly evolving market conditions call for real-time risk monitoring, but estimating it online remains challenging. In this paper, we study the online estimation of one of the most widely used risk measures, Value at Risk (VaR). Under the offline simulation online application (OSOA) framework, we formulate online VaR estimation as a conditional quantile learning problem with two key requirements: estimation accuracy and coverage reliability. To address the former, we employ quantile regression forests (QRF) to capture nonlinear and high-dimensional relationships between risk factors and conditional VaR. To address the latter, we adapt conformal prediction, conventionally used for prediction intervals, into a one-sided calibration procedure for the VaR estimator. We establish pointwise and L2 consistency for the QRF estimator, finite-sample model-free marginal coverage validity for the conformalized estimator, and asymptotic conditional coverage validity. Numerical experiments on a multi-asset option portfolio show that our proposed method becomes particularly competitive as the risk-factor dimension increases, while conformal calibration substantially corrects undercoverage. The proposed estimators also enable fast online prediction, supporting real-time risk monitoring.
For H subset of ([n] k), let v (H) denote its matching number and let d(H) (E) denote the codegree of a (k-1)-set E. We study the codegree moments co(p)(H) = Sigma(E is an element of([n] k-1)) dH(E)(p) and the number of copies of the k-uniform l-petal sunflflower S(k-l)(k-1)whose core has size k - 1. For fifixed positive integers k, l >= 2 and s, p >= 1, and all sufficiently large n, we prove that among all k-uniform families with matching number at most s, both quantities are uniquely maximized, up to permutation, by H-n,H-k,H-s = {F is an element of([n] k): F boolean AND [s] not equal empty set}. This determines the generalized Turan number ex(k)(n, S-k,l(k-1), Ms+1), where M(s+1)consists of s+ 1 pairwise disjoint edges. When k = 3, the conclusion for codegree moments holds for n >= 6s+ 3, uniformly for all positive integers p. The proof combines a theorem of Frankl and Kupavskii on families with bounded matching number, an analysis of (k - 1)-sets of large codegree, and a moment inequality. (c) 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Property rights system reform is a crucial means to stimulate rural development vitality and facilitate the strategy of rural revitalization. However, there is still insufficient empirical evidence regarding whether property rights delineation can reduce farming households’ precautionary savings and thereby boost their consumption. To address this, this study takes China’s new round of rural land rights confirmation (RLRC) as an example. It constructs a quasi-natural experiment based on data from the 2013 and 2015 China Household Finance Survey (CHFS) and the 2018 China Labor-force Dynamics Survey (CLDS). By comprehensively employing the Difference-in-Differences (DID) method, the Instrumental variable (IV) method, and the Mediation effect model, this study empirically investigates the causal relationship between RLRC and farming households’ consumption, with a particular focus on the mediating effect of precautionary savings. This study finds that the RLRC promotes the growth of farming households’ consumption, and this conclusion remains valid after undergoing various robustness tests. Mechanism analysis reveals that RLRC boosts farming households’ consumption by reducing their precautionary savings, and this mechanism remains robust and effective even after the implementation of the “separation of three rights” reform of rural land and the pilot programs for the mortgage loans of rural land management rights. Heterogeneity analysis indicates that for households with younger household heads and those possessing richer human capital and social capital, the stimulating effect of RLRC on their consumption is more pronounced. Further analysis shows that RLRC primarily promotes subsistence consumption among farming households, rather than developmental consumption, while also having a positive effect on their income improvement. This study not only provides a new explanation for the paradoxical phenomenon of “farming households having money but being reluctant to spend it” but also offers new empirical evidence for government departments to optimize or formulate consumption stimulation policies.
Global climate change and extreme precipitation events pose increasing threats to agricultural systems worldwide. However, existing studies often fail to integrate the synergistic effects of precipitation, neglect the role of transportation infrastructure, and rely on data with coarse spatial resolution. To address these gaps, this study develops a "climate-cropland-transportation" framework. By integrating high-resolution hourly precipitation data (0.1 & ring;)and 30 m cropland distribution data, we quantified the thresholds, frequency, and intensity of extreme precipitation to construct a Cropland Extreme Precipitation Exposure (CEPE) index using the entropy weighting method. Four transportation accessibility scenarios-considering the presence or absence of expressways connecting prefecture-and county-level cities-were simulated to examine their spatial coupling with the CEPE. The results reveal pronounced spatial heterogeneity in CEPE across the study area. Rural population density and industrial structure exert nonlinear regulatory effects on cropland exposure to extreme precipitation. Extreme precipitation intensity peaks at moderate population levels, while areas where the primary industry accounts for 30-40% of the economy constitute a critical buffering zone. Geographically, croplands in southwest China remain highly threatened by extreme precipitation, whereas the exposure fluctuates considerably across the Huang-Huai-Hai Plain and the Northeast China Plain. Uneven transportation accessibility further amplifies these exposures, creating vulnerability traps in regions with high exposure but low accessibility, such as the Northeast China Plain. These findings offer valuable insights for developing targeted agricultural and infrastructure strategies to strengthen agricultural resilience under climate extremes.
