A Cape Cod model for the exponential dispersion family

The defining feature of the Cape Cod algorithm in current literature is its assumption of a constant loss ratio over accident periods. This is a highly simplifying assumption relative to the chain ladder model which, in effect, allows loss ratio to vary freely over accident period.Much of the literature on Cape Cod reserving treats it as essentially just an algorithm. It does not posit a parametric model supporting the algorithm. There are one or two exceptions to this. The present paper extends them by introducing a couple of more general stochastic models under which maximum likelihood estimation yields parameters estimates closely resembling those of the classical Cape Cod algorithm.For one of these models, these estimators are shown to be minimum variance unbiased, and so are superior to the conventional estimators, which rely on the chain ladder.A Bayesian Cape Cod model is also introduced, and a MAP estimator calculated.A numerical example is included.     

Addendum to ‘The multi-year non-life insurance risk in the additive reserving model’ [Insurance Math. Econom. 52(3) (2013) 590–598]: Quantification of multi-year non-life insurance risk in chain ladder reserving models

This is the first study to derive closed-form analytical expressions for multi-year non-life insurance risk in the chain ladder model. Extending on previous research on the additive reserving model, we define multi-year risk via prediction errors of multi-year claims development results including both observed and future accident years. A resampling argument and a first-order Taylor approximation address the quantification of estimation errors and multiplicative dependencies in the chain ladder framework, respectively. From our generalized multi-year approach, we deduce estimators for reserve and premium risks in multi-year view and their implicit correlation. We reproduce well-known results from literature for the special cases of one-year and ultimo view. Further, we comment on how to obtain estimators for generalized versions of the chain ladder method. A case study demonstrates the applicability of our analytical formulae.     

Highly Efficient Multiphoton‐Pumped Frequency‐Upconversion Stimulated Blue Emission with Ultralow Threshold from Highly Extended Ladder‐Type Oligo(p‐phenylene)s

A series of highly extended π‐conjugated ladder‐type oligo(p‐phenylene)s containing up to 10 phenyl rings with (L)‐Ph(n)‐NPh (n=7–10) or without diphenylamino endcaps (L)‐Ph(n) (n=7 and 8) were synthesized and investigated for their multiphoton absorption properties for frequency upconverted blue ASE/lasing. Extremely large two‐photon absorption (2PA) cross‐sections and highly efficient 2PA ASE/lasing with ultralow threshold were achieved. (L)‐Ph(10)‐NPh exhibits the highest intrinsic 2PA cross‐section of 3643 GM for a blue emissive organic fluorophore reported so far. The record‐high 2PA pumped ASE/lasing efficiency of 2.06 % was obtained by un‐endcapped oligomer, (L)‐Ph(8) rather than that with larger σ₂, suggesting that a molecule with larger σ₂ is not guaranteed to exhibit higher η₂. All of these oligomers exhibit exceptionally ultralow 2PA pumped ASE/lasing thresholds, among which the lowest 2PA pumped threshold of circa 0.26 μJ was achieved by (L)‐Ph(10)‐NPh.     

Synthesis of Pyrene‐based Planar Conjugated Polymers and the Regioisomers by Intramolecular Cyclization

Several planar conjugated polymers and model compounds containing pyrene units are synthesized. The precursor polymers and model compounds are obtained through the Pd(0)‐catalyzed Suzuki reaction, then the planar structure is formed through intramolecular cyclization in the presence of acid. We investigate the regioisomers in intramolecular cyclization reaction by using model compounds, suggesting that the syn‐ and anti‐structures are formed in ladder‐type polymer LP1 , and the syn‐structure is more easily formed in LP3 . The planar conjugated polymers and model compounds show untypical features of ladder‐type polymers, they display broad absorption and blue or blue‐green emission in solution, and interchain π‐π stacking in film still occurs. Moreover, the new polymers and model compounds are characterized by nuclear magnetic resonance (NMR) spectroscopy, gel‐permeation chromatography (GPC) and cyclic voltammetry (CV).     

Design of a re-entrant double-staggered ladder circuit for V-band coupled-cavity traveling-wave tubes

The re-entrant double-staggered ladder slow-wave structure is employed in a high-power V-band coupled-cavity traveling-wave tube. This structure has a wide bandwidth, a moderate interaction impedance, and excellent thermal dissipation properties, as well as easy fabrication. A well-matched waveguide coupler is proposed for the structure. Combining the design of attenuators, a full-scale three-dimensional circuit model for the V-band coupled-cavity traveling-wave tube is constructed. The electromagnetic characteristics and the beam-wave interaction of this structure are investigated. The beam current is set to be 100 mA, and the cathode voltage is tuned from 16.8 kV to 15.8 kV. The calculation results show that this tube can produce a saturated average output power over 100 W with an instantaneous bandwidth greater than 1.25 GHz in the frequency ranging from 58 GHz to 62 GHz. The corresponding gain and electronic efficiency can reach over 32 dB and 6.5%, respectively.     

未决赔款准备金评估的随机性Munich链梯法

精算实务界通常采用链梯法等确定性方法评估未决赔款准备金,这些评估方法存在一定缺陷,一方面不能有效考虑保险公司历史数据中所包含的已决赔款和已报案赔款数据信息,另一方面只能得到未决赔款准备金的均值估计,不能度量不确定性。为了克服这些缺陷,本文结合Mack模型假设和非参数Bootstrap重抽样方法,提出了未决赔款准备金评估的随机性Munich链梯法,并应用R软件对精算实务中的实例给出了数值分析。     

高激发态原子的相干效应

本文以高激发态原子为研究对象, 由基态、激发态和高激发态能级形成阶梯型三能级系统, 理论上求解阶梯型三能级系统的密度矩阵方程, 研究了高激发态原子的相干效应, 计算获得探测光的吸收和色散曲线. 并研究了高激发态原子间相互作用以及外加电场对相干效应的影响. 结果表明, 外加场可以使吸收和色散曲线产生频移.     

Ladder π‐Conjugated Materials Containing Main‐Group Elements

Ladder π‐conjugated compounds, which have fully ring‐fused polycyclic skeletons, are an important class of materials possessing significant potentials for application in organic electronics. The incorporation of main‐group elements, such as B, Si, P, S, and Se, into the ladder skeletons as bridging moieties is a powerful strategy to endow unusual electronic structures as well as suitable molecular arrangements in the solid state, giving rise to attractive photophysical and electronic properties. Recent efforts have produced a number of fascinating ladder materials, some of which indeed showed high performance as light‐emitting materials and charge carrier transporting materials. This Focus Review is an overview of the progress in this chemistry, focusing on several important π‐conjugated skeletons.