Insurance Premium Prediction via Gradient Tree-Boosted Tweedie Compound Poisson Models

The Tweedie GLM is a widely used method for predicting insurance premiums. However, the structure of the logarithmic mean is restricted to a linear form in the Tweedie GLM, which can be too rigid for many applications. As a better alternative, we propose a gradient tree-boosting algorithm and apply it to Tweedie compound Poisson models for pure premiums. We use a profile likelihood approach to estimate the index and dispersion parameters. Our method is capable of fitting a flexible nonlinear Tweedie model and capturing complex interactions among predictors. A simulation study confirms the excellent prediction performance of our method. As an application, we apply our method to an auto-insurance claim data and show that the new method is superior to the existing methods in the sense that it generates more accurate premium predictions, thus helping solve the adverse selection issue. We have implemented our method in a user-friendly R package that also includes a nice visualization tool for interpreting the fitted model.     

科学发展的梯度理论与我国改革开放30年的发展战略

科学发展的梯度理论是科学发展观的一个新领域。研究这个新领域,有助于对我国改革开放30年来经济社会的发展作一全景式观照。坚持科学发展的梯度性,是改革开放30年来我党的一个重要战略。坚持在科学发展观指导下研究我国不同发展阶段的个性化特征以及这些特征的影响,揭示我国经济社会发展的梯度性规律,是时代的选择。科学发展的梯度理论在于从发展梯度的角度阐述科学发展观,研究科学发展的规律,研究科学发展过程中人与自然、人与社会、人与人、人与自身的问题,关注科学发展的中间过程状态,论证我国经济社会发展的合规律性与必然逻辑,探索科学发展过程的创造性和谐,为科学发展的未来阶段提供理论支持。我国梯度发展的战略决策是"三步走"与"台阶式",其划分阶段的方法论指导是借鉴非线性过程理论;其划分阶段的量化参照是借鉴经济发展短周期理论。科学发展的梯度理论把改革开放以来我国经济社会的发展划分为三个阶段:以"反贫困"为特征的经济社会发展初级阶段;以"重效益"为特征的经济社会发展跨越阶段;以"讲和谐"为特征的经济社会发展逐步完善阶段。     

一类新的自适应非单调谱投影梯度法

给出了求解凸约束优化的一类新的自适应非单调谱投影梯度法.通过引入具有自适应性的权重参数,使算法在迭代过程中能自动调节非单调策略. 在适当条件下证明了算法的收敛性.数值试验结果表明,该算法在一定程度上能减少在线搜索过程中对非单调参数M的依赖.     

On the Internal Structure of Cities

We prove the existence of a symmetric equilibrium in a circular city in which businesses and housing can both be located anywhere in the city. In this equilibrium, firms balance the external benefits from locating near other producers against the costs of longer commutes for workers. An equilibrium city need not take the form of a central business district surrounded by a residential area. We propose a general algorithm for constructing equilibria, and use it to study the way land use is affected by changes in the model's underlying parameters.