物理科学发展史的回顾与聚集力学的创建

本文简单地阐述了物理科学的发展电,在19世纪末期,物珲科学已经有相当发展,并形成了三个科学分支--研究物体运动,有牛顿力学;研究物质热运动,有热力学和统计力学;研究电磁波和光波,有电动力学,可是,这三种经典力学在20世纪初面临着新的挑战(困难),从而,相应地产生了三种新的基础理论,即狭义相对论,广义相对论;聚集理论,聚集力学;量子理论,量子力学,具体实践表明,它们在解决新的难题方面都取得很大成功.     

具限制投资组合和交易费用的博弈未定权益的保值

博弈期权是由kifer(2000)提出的,但就其本质而言,仍是美式期权的一种,只是增加了卖方中止合约的权利.本文主要对连续市场模型中具交易费用和限制投资组合的博弈未定权益的保值问题进行了研究,给出了买卖双方的保值价格和一个无套利区间.     

复合Poisson模型中“双界限”分红问题

引入了复合Poisson模型中的"双界限"分红模型,在这种模型中,当盈余超过上限时分红以不超过保费率的速率付出,低于下限后保费率增大.文中利用Gerber- Shiu函数来分析这种模型,先导出了Gerber-Shiu函数m_1,m_2,m_3满足的积分-微分方程,再给出m_1,m_2,m_3的解析表示,最后通过几步把Gerber-Shiu函数m(u;b_1,b)的解析式表示出来.     

保险管理决策中的两个问题

本文运用风险决策理论建立了分保限额与红利分派两个保险管理决策问题的数学模型,从理论和实践两个方面讨论了最优管理策略,并给出了计算实例。     

Constant dividend barrier in a risk model with interclaim-dependent claim sizes

The risk model with interclaim-dependent claim sizes proposed by Boudreault et al. [Boudreault, M., Cossette, H., Landriault, D., Marceau, E., 2006. On a risk model with dependence between interclaim arrivals and claim sizes. Scand. Actur. J., 265-285] is studied in the presence of a constant dividend barrier. An integro-differential equation for some Gerber-Shiu discounted penalty functions is derived. We show that its solution can be expressed as the solution to the Gerber-Shiu discounted penalty function in the same risk model with the absence of a barrier and a combination of two linearly independent solutions to the associated homogeneous integro-differential equation. Finally, we analyze the expected present value of dividend payments before ruin in the same class of risk models. An homogeneous integro-differential equation is derived and then solved. Its solution can be expressed as a different combination of the two fundamental solutions to the homogeneous integro-differential equation associated to the Gerber-Shiu discounted penalty function.     

Sample path large and moderate deviations for risk model with delayed claims

Sample path large and moderate deviation principles for Markov modulated risk models with delayed claims are proved by the exponential martingale method. As applications, asymptotic estimates and exponential bounds of the ruin probability are also studied.     

Physical boundaries within aggregates – differences between amorphous,para‐crystalline,and crystalline Structures

The structural properties of finely divided inorganic materials such as metal and metalloid oxides, silicates or carbonates of both synthetic and natural origin are compared by means of electron microscopy and tomography. The structure of the outer surfaces of various compact or compacted agglomerates may suggest some striking similarities between various amorphous silica on the one hand and crystalline titania and alumina on the other however the details of the interior fine structure are completely different. Inside of the crystalline aggregates of, for example, alumina and titania distinct grain boundaries between the inter‐grown primary crystallites exist. Also physical boundaries between different solid phases and crystalline/amorphous transitions in core/shell structures can occur. No physical grain or phase boundaries were found inside of synthetic amorphous silica or para‐crystalline carbon black thus, the aggregate is the constituent particle. Synthetic amorphous silica from different production technologies (fumed/pyrogenic, precipitated, aerogel, gel) may exhibit different macro‐morphology but distinct similarities of the amorphous silica networks. Computational studies on silica and titania underline the stability of constituent particles and aggregates as observed by means of TEM after dispersing the original materials by ultra‐sonication.     

基于巨灾模型的巨灾保险组合研究

巨灾风险所造成的巨大损失已经威胁到人类社会的可持续发展.巨灾保险是分散巨灾损失的一种途径,利用巨灾模型研究被保风险的累积损失和个人损失分布的数学性质,且考虑损失率是巨灾强度的函数.通过巨灾模型和保险公司破产概率的计算和数值仿真,得到不能仅仅依靠保费的选择而分散巨灾风险.     

一类相依风险模型的破产问题

本文研究了一类索赔过程与索赔额大小相关的风险模型.利用无穷小方法,得到了该相依模型的折扣惩罚函数的期望满足的方程.及其拉普拉斯变换的表达式.并且给出指数索赔时的具体运用.     

Optimal policy for a two-facility inventory problem with storage constraints and two freight modes

This paper considers a two-facility supply chain for a single product in which facility 1 orders the product from facility 2 and facility 2 orders the product from a supplier in each period. The orders placed by each facility are delivered in two possible nonnegative integer numbers of periods. The difference between them is one period. Random demands in each period arise only at facility 1. There are physical storage constraints at both facilities in each period. The objective of the supply chain is to find an ordering policy that minimizes the expected cost over a finite horizon and the discounted stationary expected cost over an infinite horizon. We characterize the structure of the minimum expected cost and the optimal ordering policy for both the finite and the discounted stationary infinite horizon problems.