Lapse risk in life insurance: Correlation and contagion effects among policyholders’ behaviors

The present paper proposes a new methodology to model the lapse risk in life insurance by integrating the dynamic aspects of policyholders’ behaviors and the dependency of the lapse intensity on macroeconomic conditions. Our approach, suitable to stable economic regimes as well as stress scenarios, introduces a mathematical framework where the lapse intensity follows a dynamic contagion process, see Dassios and Zhao (2011). This allows to capture both contagion and correlation potentially arising among insureds’ behaviors. In this framework, an external market driven jump component drives the lapse intensity process depending on the interest rate trajectory: when the spread between the market interest rates and the contractual crediting rate crosses a given threshold, the insurer is likely to experience more surrenders. A log-normal dynamic for the forward rates is introduced to build trajectories of an observable market variable and mimic the effect of a macroeconomic triggering event based on interest rates on the lapse intensity. Contrary to previous works, our shot-noise intensity is not constant and the resulting intensity process is not Markovian. Closed-form expressions and analytic sensitivities for the moments of the lapse intensity are provided, showing how lapses can be affected by massive copycat behaviors. Further analyses are then conducted to illustrate how the mean risk varies depending on the model’s parameters, while a simulation study compares our results with those obtained using standard practices. The numerical outputs highlight a potential misestimation of the expected number of lapses under extreme scenarios when using classical stress testing methodologies.     

Stadium型介观器件腔中粒子逃逸率的研究

本文研究了粒子在二维弱开口的Bunimovich Stadium型介观混沌器件中的逃逸规律.利用经典统计的方法,通过改变器件端口宽度、圆弧半径及器件腔长等参数,首次发现随器件各项参数变化的分形维数与粒子逃逸率趋势符合,并揭示了混沌体系的逃逸指数受器件形状的影响.统计并拟合了粒子逃逸率与粒子波数大小的关系,数值结果表明,粒子逃逸率与波数为二次函数关系,但逃逸率与能量大小不是严格的线性关系.进一步分析了在器件入口处粒子的衍射效应对粒子逃逸的影响,结果表明,衍射效应使粒子逃逸率增加,且粒子数的演化在时间较短时不再满足指数关系,长时间的演化再次满足指数衰减规律.     

二维Hénon-Heiles势及其变形势体系逃逸率与分形维数的研究

采用Chin和Chen的动力学算法追踪粒子在体系中的运动情况, 首次研究并对比了粒子在Hénon-Heiles体系与变形Hénon-Heiles六边形体系中的混沌逃逸规律, 在Hénon-Heiles体系中, 对于不同能量范围, 分形维数与逃逸率随能量而改变, 但在变形Hénon-Heiles六边形体系中, 仅在低能区分形维数与逃逸率随能量的改变而变化, 而高能区逃逸率和分形维数趋于稳定值. 并且得到普遍规律, 即不同混沌体系中粒子的混沌逃逸率和粒子逃逸的分形维数呈现较强的线性相关性. 因而分形维数可以作为工具研究混沌体系中粒子的逃逸规律, 在介观器件设计中可以通过研究混沌电子器件的分形维数来表征粒子在器件中的传输行为.     

High-Precision Spectroscopy of Antiprotonic Helium – First Results from the AD of CERN

New results of the laser and microwave spectroscopy of antiprotonic helium “atomcules” obtained in the first year of operation of the Antiproton Decelerator (AD) facility of CERN are presented. They include the discovery of three new resonant transitions and the determination of the zero-density wavelength of six transitions with an accuracy of 130 ppb in the best case. Auger rates of those states were also determined, and two of them were found to be several orders of magnitude larger than expected from a simple estimate based on the multipolarity Δl, i.e., the jump in angular momentum required for the antiproton to reach the next lower-lying state of ionized He⁺⁺. Furthermore, a first signal of a two-laser microwave triple resonance to measure the hyperfine splitting in antiprotonic helium was observed. This revised version was published online in August 2006 with corrections to the Cover Date.     

The estimation of a nonlinear moving average model

We consider discrete-parameter stochastic processes that are the output of a nonlinear filter driven by white noise. For a simple model, we derive estimates of the unknown coefficients in the transfer function and the noise variance, and investigate their asymptotic properties. We prove some lemmas that can also be used to obtain rates of convergence in the weak and strong laws of large numbers, and central limit theorems, for estimates of more general nonlinear models.     

Transient behavior of entangled polymers at high shear rates

A new model is presented for describing the time-dependent flow of entangled polymer liquids at high shear rates. The results were obtained by extending the Doi and Edwards theory to include the effect of chain stretching. This nonlinear phenomenon is predicted to occur when the product of the shear rate and longitudinal relaxation time of the polymer exceeds one. If a constant-shear-rate flow is started under these conditions, it is shown that the shear stress and the normal stress are considerably larger than that predicted by the original reptation model. We also find that both of these stresses can pass through maxima before reaching a steady state and that the times required to reach these maxima are constants independent of the shear rate. In general the new model requires the numerical solution of coupled partial differential equations. However, at the highest shear rates where reptative relaxation is no longer important, an analytical solution for the stresses is found. The results obtained here are shown to agree well with experimental data and to be an improvement over a simpler model recently proposed.