This study aims to locate the knots of cumulative coronavirus disease 2019 (COVID-19) case number during the first-level response to public health emergency in the provinces of China except Hubei. The provinces were grouped into three regions, namely eastern, central and western provinces, and the trends between adjacent knots were compared among the three regions. COVID-19 case number, migration scale index, Baidu index, demographic, economic and public health resource data were collected from 22 Chinese provinces from 19 January 2020 to 12 March 2020. Spline regression was applied to the data of all included, eastern, central and western provinces. The research period was divided into three stages by two knots. The first stage (from 19 January to around 25 January) was similar among three regions. However, in the second stage, growth of COVID-19 case number was flatter and lasted longer in western provinces (from 25 January to 18 February) than in eastern and central provinces (from 26 February to around 11 February). In the third stage, the growth of COVID-19 case number slowed down in all the three regions. Included covariates were different among the three regions. Overall, spline regression with covariates showed the different change patterns in eastern, central and western provinces, which provided a better insight into regional characteristics of COVID-19 pandemic.

A variable annuity (VA) is an equity-linked annuity that provides investment guarantees to its policyholder and its contributions are normally invested in multiple underlying assets (e.g., mutual funds), which exposes VA liability to significant market risks. Hedging the market risks is therefore crucial in risk managing a VA portfolio as the VA guarantees are long-dated liabilities that may span decades. In order to hedge the VA liability, the issuing insurance company would need to construct a hedging portfolio consisting of the underlying assets whose positions are often determined by the liability Greeks such as partial dollar Deltas. Usually, these quantities are calculated via nested simulation approach. For insurance companies that manage large VA portfolios (e.g., 100k+ policies), calculating those quantities is extremely time-consuming or even prohibitive due to the complexity of the guarantee payoffs and the stochastic-on-stochastic nature of the nested simulation algorithm. In this paper, we extend the surrogate model-assisted nest simulation approach in Lin and Yang [(2020) Insurance: Mathematics and Economics, 91, 85–103] to efficiently calculate the total VA liability and the partial dollar Deltas for large VA portfolios with multiple underlying assets. In our proposed algorithm, the nested simulation is run using small sets of selected representative policies and representative outer loops. As a result, the computing time is substantially reduced. The computational advantage of the proposed algorithm and the importance of dynamic hedging are further illustrated through a profit and loss (P&L) analysis for a large synthetic VA portfolio. Moreover, the robustness of the performance of the proposed algorithm is tested with multiple simulation runs. Numerical results show that the proposed algorithm is able to accurately approximate different quantities of interest and the performance is robust with respect to different sets of parameter inputs. Finally, we show how our approach could be extended to potentially incorporate stochastic interest rates and estimate other Greeks such as Rho.

Competitiveness of noogoora burr and fierce thornapple in irrigated cotton was assessed using area-of-influence methodology. Lint yields were regressed against distances from the weeds using spline regression. The resulting regression curves were used to estimate areas of influence and yield losses, which were further modeled as functions of weed size to understand weed competitiveness. Cotton lint yield reductions averaged 36 and 12%, with maximum distances of influence of 1.71 and 1.65 m for noogoora burr and fierce thornapple, respectively. Economic thresholds for control using hand hoeing were related to weed size. Thresholds for average-size weeds were one cocklebur in 195 m and one fierce thornapple in 73 m of cotton row.

We compared exotic pasture grass cover near the edges of 20–25-y-old secondary forests (N = 8) with those of mature forests (N = 8), bordering actively grazed pastures on the Pacific Coast of Ecuador. We estimated grass cover in 224 1 × 3-m plots along transects that ran from the pasture edge into forest interiors (11–44 m). Using a spline regression, we divided the transects into three segments: exterior (in the pasture), edge and interior (in the forest). With a stepwise regression, we tested the effect of transect section, forest type and distance from edge on grass cover. Forest type, distance from edge, interior transect section and the combined effect of distance from edge in both the interior and exterior sections explained variation in grass cover. Grass abundance was higher and penetrated further into secondary than mature forests. Edge proximity and differences in forest canopy openness likely favours recruitment and persistence of pasture grasses.