带有随机干扰和确定投资回报风险过程下的一些分布

我们考虑既带有随机干扰又带有确定投资回报的风险过程, 得到了破产前瞬间盈余的分布$F_{\delta}(u,x)$及破产前瞬间盈余和破产时赤字的联合分布$H_{\delta}(u,x,y)$所满足的积分表达, 连续性及二次连续可微性和积分--微分方程. 同时, 只有随机干扰的风险模型下的破产前瞬间盈余的分布及破产前瞬间盈余和破产时赤字的联合分布所满足的性质也被得到. 已有文献中的诸多有关结果均可以通过令我们结论中的某些参数特殊化为零而得到.     

随机利率作用下的经典风险模型的破产概率

本文讨论了在随机利率作用下经典风险模型的破产问题,给出了导致公司破产的索赔额的L ap lace变换所满足的微分方程,给出了破产概率二次连续可微性的条件,得到了导致公司破产的所满足的积分微分方程;破产时刻公司赤字的L ap lace变换所满足的积分-微分方程.作为特例,本文给出了当索赔为指数分布地导致破产索赔额的L ap lace变换和破产时刻赤字的L ap lace变换的微分方程.     

投资和干扰具有随机保费的离散风险模型

在考虑具有保费且含通货膨胀等随机干扰因素的影响,同时又考虑将多余资本用于投资以提高保险公司赔付能力的基础上,对经典的风险模型进行扩展,由此建立了一个带有投资且具有随机保费率和干扰的更为实际的风险模型.对新模型的性质进行讨论,得到了其盈利过程的平稳增量性和风险过程的统计特征:对破产概率的研究,获得了最终破产概率的LunGlberg不等式及其一般表达式.最后通过数值模拟阐述了破产概率上界分别随投资额、保费额和理赔额变化而变动的情况,获得了对实际运营有启发性的结论.     

带扰动的随机保费模型的渐近最优投资

本文研究了一类具有随机投资回报的随机保费模型的最小破产概率的渐近性质.在假定常值投资策略的情形下,通过最小化调节系数,我们得到了与此调节系数相对应的最优的常值投资策略.最后我们证明当初始盈余趋向于无穷的时候,最优的投资策略趋向于这个常值策略.     

随机利率下具有马氏调控的Pascal模型

收稿研究随机环境下带利率的风险模型;对随机利率下由马氏调控费率的Pascal模型,我们克服了随机环境和随机利率的限制,得到破产概率及破产时、破产前剩余、破产赤字联合分布的计算方法.     

随机利率下的Erlang(2)风险模型

本文主要对索赔记数过程是Erlang(2)过程,随机利率为一个L啨vy过程的风险模型进行了讨论.首先导出了破产概率满足的积分方程,估计了其上下界,然后针对随机利率为布朗运动以及漂移布朗运动的情况导出了破产概率满足的具体积分方程,最后讨论了罚金函数,并写出了罚金函数满足的积分方程以及在特殊情况下满足的积分微分方程.     

基于随机波动的企业的最优组合投资策略

Merton的投资模型拓展到随机波动模型.在典型的动态规划中,投资问题中的值函数一般用Bellman方程的粘滞解表示.本文通过指数变换把偏微分方程转变成一个半线性的抛物线方程,并证明了其值函数连续解的存在性,在此基础上给出了企业的最优组合投资策略及一个投资的例子.     

随机脉冲随机微分方程解的存在唯一性

提出了随机脉冲随机微分方程模型,其中所谓的随机脉冲是指脉冲幅度由随机变量序列驱动,并且脉冲发生的时间也是一个随机变量序列.因此,随机脉冲随机微分方程是对带跳的随机微分方程模型的推广.利用Gronwall不等式、Lipschtiz条件和随机分析技巧,得到了随机脉冲随机微分方程的解的存在唯一性条件.     

随机环境下风险模型的破产问题

本文研究了在随机环境下风险模型的破产问题.利用递归方法,获得了破产前盈余的分布和描述破产严重性的预警区的分布, 推广了已有结果.     

一类随机保费率下的风险模型

引入随机变量保费率,对古典风险模型进行推广,主要研究随机保费率下的风险模型,用随机过程和鞅论的方法得出破产概率、末离前最大盈余分布、破产前瞬时盈余与破产赤字的联合分布等精算量分布的具体表达式.     

具有随机收入的扰动更新风险模型(英文)

本文研究了一类随机收入的扰动更新风险模型的破产问题.运用拉普拉斯变换以及拉格朗日差值公式得到了Gerber-Shiu函数的拉普拉斯变换的渐近表达式,推广了文献[4]中的结论.     

The expected discounted penalty function under a renewal risk model with stochastic income

In this paper, we consider a renewal risk model with stochastic premiums income. We assume that the premium number process and the claim number process are a Poisson process and a generalized Erlang (n) processes, respectively. When the individual stochastic premium sizes are exponentially distributed, the Laplace transform and a defective renewal equation for the Gerber-Shiu discounted penalty function are obtained. Furthermore, the discounted joint distribution of the surplus just before ruin and the deficit at ruin is given. When the claim size distributions belong to the rational family, the explicit expression of the Gerber-Shiu discounted penalty function is derived. Finally, a specific example is provided.     

The Distribution of the Maximum Surplus before Ruin for Two Classes of Perturbed Risk Model with Stochastic Income

In this paper, we consider the two classes of perturbed risk model with stochastic income. We set up the integro-differential equations for the distribution of the maximum surplus before ruin $\mathscr{G}(u;d). The Laplace transforms of $\mathscr{G}(u;d),d\rightarrow+\infty are obtained for exponential premium income. The explicit expressions for the distribution of the maximum surplus before ruin are derived when the two classes claim amount distributions all belong to the rational family.     

带干扰的保费随机收取的双险种风险模型

推广了已有文献中提出的带干扰的双险种复合负二项风险模型,让保费收取次数服从负二项分布,两类险种的索赔也服从负二项分布,得到了带干扰的保费随机收取的双险种风险模型,给出了破产概率的一般表达式和上界．     

Ruin problems with stochastic premium stochastic return on investments

In this paper, ruin problems in the risk model with stochastic premium incomes and stochastic return on investments are studied. The logarithm of the asset price process is assumed to be a Lévy process. An exact expression for expected discounted penalty function is established. Lower bounds and two kinds of upper bounds for expected discounted penalty function are obtained by inductive method and martingale approach. Integro-differential equations for the expected discounted penalty function are obtained when the Lévy process is a Brownian motion with positive drift and a compound Poisson process, respectively. Some analytical examples and numerical examples are given to illustrate the upper bounds and the applications of the integro-differential equations in this paper.      

On a risk model with stochastic premiums income and dependence between income and loss

Labbé and Sendova (2009) [9] consider a compound Poisson risk model with stochastic premiums income. In this paper, we extend their model by assuming that there exists a specific dependence structure among the claim sizes, interclaim times and premium sizes. Assume that the distributions of the premium sizes and interclaim times are controlled by the claim sizes. When the individual premium sizes are exponentially distributed, the Laplace transforms and defective renewal equations for the (Gerber-Shiu) discounted penalty functions are obtained. When the individual premium sizes have rational Laplace transforms, we show that the Laplace transforms for the discounted penalty functions can also be obtained.     

具有随机波动的最优消费—投资模型

本文讨论了具有交易成本与时变波动的最优投资问题。在此模型中,当风险溢价与方差成线性关系时,最优策略与波动水平无关。     

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与经典Cramer-Lundberg风险模型中保费收取过程 是时间的线性函数不同, 我们考虑聚合的保费收取过程是复合Poisson过程, 研究了在此模型下的常数分红策略问题. Dickson和Waters,(2004)指出在破产发生时, 股东还应有责任偿付破产时的赤字. 因此, 在本文中考虑的最优准则是最大化破产发生前的分红折现值与破产发生时赤字的差的期望. 做为例子, 当个体保费收取额和索赔额均为指数分布时, 给出了计算分红障碍的条件     

On the Gerber-Shiu Function and Optimal Dividend Strategy for a Thinning Risk Model

In this paper, the risk model under constant dividend barrier strategy is studied, in which the premium income follows a compound Poisson process and the arrival of the claims is a p-thinning process of the premium arrival process. The integral equations with boundary conditions for the expected discounted aggregate dividend payments and the expected discounted penalty function until ruin are derived. In addition, the explicit expressions for the Laplace transform of the ruin time and the expected aggregate discounted dividend payments until ruin are given when the individual stochastic premium amount and claim amount are exponentially distributed. Finally, the optimal barrier is presented under the condition of maximizing the expectation of the difference between discounted aggregate dividends until ruin and the deficit at ruin.