具有红利边界的Erlang（2）风险模型

给出了具有边界红利策略的Erlang（2）风险模型,在此红利策略下,若保险公司的盈余在红利线以下时不支付红利,否则红利以低于保费率的常速率予以支付．对于该模型,本文推导了Gerber-Shiu折现惩罚函数所满足的两个积分－微分方程和更新方程．     

常数红利边界下的一类马氏风险模型

本文研究了常数红利边界下一类马氏风险模型的红利派发矩,破产前所有红利的分布等相关问题.利用更新方法,给出了该模型破产前红利折现的期望满足的微分-积分方程,得到破产前所有红利的分布.通过构造特殊的初始条件,得到了相关的方程组解,推广了文献[3]的结果.     

带常数红利边界马氏相依风险模型的Gerber-Shiu折扣惩罚函数的期望

本文研究了带常数红利边界的马氏相依风险模型,利用微分方法,推导出折扣惩罚函数的期望所满足的积分-微分方程,及其满足的边界条件,并给出了其解的一般表达形式.     

带红利线的双复合Poisson过程风险模型的破产概率

在考虑红利付款下,将经典风险模型推广为双复合Po isson过程模型,应用鞅论的方法,得出了最终破产概率和Lundberg不等式.     

带常数边界的平衡更新风险模型的破产问题

本文讨论带常数边界的平衡更新风险模型的破产问题.利用Markov性质,给出惩罚函数满足的积分-微分方程,证明其惩罚函数可由更新风险模型的惩罚函数表示,并且给出一个具体的例子.     

相关的常数红利障碍Poisson-Erlang风险模型(英文)

本文研究了有常数红利障碍的相关聚合理赔风险模型.利用Laplace变换和逆Laplace变换的方法,获得了该模型中罚金折现期望函数的积分一微分方程的解法,推广了一类积分-微分方程的求解方法.     

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.     

常红利边界复合二项模型红利期望现值

在完全离散的复合二项风险模型基础上,考虑常红利边界策略下的红利支付问题．通过两种不同的方法,得到了红利期望现值所满足的两个方程．由这些方程特殊性质,在比较宽松的条件下,通过建立相应的迭代过程,求解出了直到破产发生时红利期望现值的近似值．     

常数红利下索赔到达时间间距为混合分布的罚金折现期望函数

在常数红利策略下考虑索赔时间间隔为指数分布与Erlang(2)分布混合时的风险模型,在此红利策略下,若保险公司的盈余在红利线以下时不支付红利,否则红利以等于保费率的常速率予以支付.对于此风险模型,推导并求解了罚金折现期望函数所满足的微积分方程,并在索赔量为指数分布时研究了其解的形式.     

具有随机投资收益的离散风险模型的最优红利分配

本文讨论的是离散模型下以期望累计红利最大化为目标的最优红利分配政策,通过Bellman最优性准则,我们得到了最优值函数满足的动态规划方程并结合实例给出了求解这些方程的算法.     

脉冲积分-微分系统零解稳定性的新的Razumikhin型定理

为研究积分-微分系统的稳定性,运用Lyapunov函数直接方法并借助Razumikhin技巧的思想,通过减弱Lyapunov函数沿系统解的导数须常负或定负的限制条件,给出了判断脉冲积分-微分系统零解稳定性的新的直接判定定理.     

Maximal B-Regular Integro-Differential Equation

By using Fourier multiplier theorems, the maximal B-regularity of ordinary integro-differential operator equations is investigated. It is shown that the corresponding differential operator is positive and satisfies coercive estimate. Moreover, these results are used to establish maximal regularity for infinite systems of integro-differential equations.     

中立多变时滞Volterra型随机动力系统的稳定性

探讨了一类非线性随机积分微分动力系统,并通过Banach不动点方法,给出了该系统零解均方渐近稳定的充要条件,形成了中立多变时滞Volterra型随机积分微分动力系统零解均方渐近稳定性定理。与前人的研究方法不同,该文根据多变时滞随机动力系统各时滞的特点,灵活构造算子,相比以往文献的方法更加灵活实用。文章的结论一定程度上改进和发展了相关研究论文的结果。另外,文章所得结论补充并推广了不动点方法在研究非线性中立多变时滞Volterra型随机积分微分动力系统零解稳定性方面的成果。     

Criteria for the well-posedness of a linear two-point boundary value problem for systems of integro-differential equations

We consider a linear two-point boundary value problem for systems of integro-differential equations. By using the parametrization method and an approximation of the integro-differential equation by a loaded differential equation, we establish coefficient tests for the well-posedness of the considered problem and suggest an algorithm for finding the solution.     

Analytic expansion of periodic solutions of integro-differential systems

We constructively obtain conditions for the existence of periodic solutions of systems of integro-differential equations in the degenerate case. By using integro-differential equations with a parameter, we construct an analytic representation of the solutions and obtain estimates for the convergence rate of iterative processes and for the exact solutions.     

On the Properties of Rings of Integro-Differential Operators and Their Corresponding Equations

Mathematical Notes - The paper deals with systems of linear integro-differential equations, including systems with a matrix identically degenerate in the domain at the highest derivative of the...     

Smooth solution of partial integro-differential equations using radial basis functions

In this work, we present the method based on radial basis functions to solve partial integro-differential equations. We focus on the parabolic type of integro-differential equations as the most common forms including the ``\emph{memory}'' of the systems. We propose to apply the collocation scheme using radial basis functions to approximate the solutions of partial integro-differential equations. Due to the presented technique, system of linear or nonlinear equations is made instead of primary problem. The method is efficient because the rate of convergence of collocation method based on radial basis functions is exponential. Some numerical examples and investigation of the experimental results show the applicability and accuracy of the method.     

Error estimates and stability of itô-type systems of nonlinear stochastic integro-differential equations

By developing an integral representation of a function of solution process of a system of Ito-type stochastic nonlinear integro-differential equations, the error estimates on absolute p-th deviation of a solution process with the solution of the mean of the corresponding deterministic system of integro-differential equations is analyzed. Furthermore, the p-th moment stability properties of the steady state of the system is studied. The obtained results would provide a partial solution to one of the fundamental problems in modelling of dynamic systems, namely, to what extent incorporating randomness in the system causes the change in behavior of the system relative to its deterministic version     

Upper and lower bounds for solutions of generalized two-point boundary value problems

This paper is concerned with two-point boundary value problems for systems of differential equations and integro-differential equations. If ?, ψ and Φ, Ψ are functions which satisfy certain differential (integro-differential) inequalities, then the given problem has a solutionu ^* such that ?≦u ^*≦ψ and Φ≦u ^*′≦Ψ.     

On the numerical solution of linear and nonlinear volterra integral and integro-differential equations

Sinc bases are developed to approximate the solutions of linear and nonlinear Volterra integral and integro-differential equations. Properties of these sinc bases and some operational matrices are first presented. These properties are then used to reduce the integral and integro-differential equations to systems of linear or nonlinear algebraic equations. Numerical examples illustrate the pertinent features of the method and its applicability to a large variety of problems. The examples include convolution type, singular as well as singularly-perturbed problems.