The gerber-shiu expected discounted penalty function for Lévy insurance risk processes

In this paper,we study a general Lévy risk process with positive and negative jumps.A renewal equation and an infinite series expression are obtained for the expected discounted penalty function of this risk model.We also examine some asymptotic behaviors for the ruin probability as the initial capital tends to infinity.     

Unified characteristic numbers and solutions of equations for birth and death processes with barriers

The state 0 of a birth and death process with state space E = {0, 1, 2,....} is a barrier which can be classified into four kinds： reflection, absorption, leaping reflection, quasi-leaping reflection. For the first, second and fourth barriers, the characteristic numbers of different forms have been introduced. In this paper unified characteristic numbers for birth and death processes with barriers were introduced, the related equations were solved and the solutions were expressed by unified characteristic numbers. This paper concerns work solving probability construction problem of birth and death processes with leaping reflection barrier and quasi-leaping reflection barrier.     

Dirichlet Forms Associated with Linear Diffusions

One-dimensional local Dirichlet spaces associated with linear diffusions are studied. The first result is to give a representation for any 1-dim local, irreducible and regular Diriehlet space. The second result is a necessary and sufficient condition for a Diriehlet space to be regular subspace of another Dirichlet space.     

带双阈值的一类更新风险模型的Gerber-Shiu折现罚函数

本文考虑一类索赔时间间隔为Erlang(2)分布的"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,得到了关于Gerber-Shiu罚金折现期望函数满足的积分-微分方程以及更新方程,进一步讨论了更新方程的解.     

跳过程的μ-不变测度-含单瞬时态情形

μ-不变测度是随机过程中一类重要的测度.首先,本文得到了含有单瞬时态的q-过程存在性定理,并进-步说明了在一些特殊情况下可以只对q-对加条件,定理仍成立.然后,对给了含单瞬时态q-对的μ-不变测度,何时存在q-过程P(t),使得π是P(t)的μ-不变测度的问题进行了讨论研究,并给出了一个充分条件.     

DURATION OF NEGATIVE SURPLUS FOR A TWO STATE MARKOV-MODULATED RISK MODEL

We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.     

关于股票价格模型的假设检验

股票模型是人们用来描述股票价格波动特征的重要工具,包括Black-scholes'模型,随机波动率模型和更一般化的指数Lévy过程模型等.同时,一些流行的技术指标(例如布林带,RSI,ROC)被股市交易者广泛使用.交易者将每日(小时,周)实际股价作为计算某个技术指标的样本,通过观察相关频率指导投资.技术指标的有效性已在实际应用中得到充分验证.已有研究成果证明股价模型成立时,一些常用的技术指标有良好的统计性质,从而解释了技术分析的合理性.本文将从另一个角度出发,利用技术指标ROC的历史数据,拒绝股票价格波动服从指数Lévy过程模型的假设.     

一类相依正态序列超过数点过程的渐近分布

{X_n,n≥1}为存在样本缺失的标准化平稳正态序列,相关系数r_n=EX_1X_(1+n).(?)_n与(?)_n分别为观测到与未观测到的子样形成的超过数点过程.令N_n=(?)_n+(?)_n.本文研究r_nln→ρ∈[0,∞)时超过数点过程N_n,(?)_n与(?)_n的弱收敛性及顺序统计量的联合渐近分布.     

可数多个Brown运动驱动的带跳随机微分方程

本文研究了由可数个Brown运动驱动的带跳随机微分方程.利用线性逼近(即Picard迭代)方法,在非Lipsclritz系数的条件下得到该类方程的解的存在性及唯一性.     

排它过程在加权图上的存在性

本文考虑图上的排它过程,每条边对应于粒子的运动.利用算子半群的方法,给出了与排它过程生成元对应的马尔科夫过程存在的充分条件.