具有常量红利界的带干扰项的风险模型及最优红利界

对于保险公司来说,如何确定其红利策略,使得投保人利益最大化是一个需要研究的课题.研究了具有常量红利界的带干扰项的经典风险模型下,索赔量为混合指数分布情形时的最优红利界的计算方法.     

具有随机消费的带恒定红利界的对偶干扰风险模型

考虑了具有随机消费的带恒定红利界的对偶干扰风险模型.分别建立了破产前红利支付与期望折现罚函数所满足的积分-微分方程.当消费量与收入量均为指数分布时,得到了破产前红利支付与破产时间的解析表达式,并列举了数值例子.     

带资本注入、交易费和税的经典风险模型的最优联合分红与注资策略（英文）

在风险理论中,经典Cramér-Lundberg模型的最优红利策略和最优红利收益函数问题是一个被广泛讨论的话题.本文讨论一类Cramér-Lundberg模型:其在分红时伴随比例赋税与固定交易费,注资时伴随比例罚金与固定交易费,并研究了其净红利收益与注入资本之差的预期贴现值的最大化问题.这里我们不允许负盈余或破产的发生.通过解相应的拟变分不等式,在索赔为指数分布时,得到了最优收益函数和最优联合分红与注资策略的解析解.     

具有常数红利边界的两类索赔相关风险模型数

研究常数红利边界下两类索赔相关的风险模型,两类索赔计数过程分别为独立的Poisson过程和广义Erlang(2)过程.利用分解Gerber-Shiu函数的方法,得到了Gerber-Shiu函数满足的积分-微分方程、边界条件、解析表达式及两类索赔额均服从指数分布时的破产概率表达式.     

阈红利策略下带干扰对偶风险模型的Gerber-Shiu罚金函数

研究了带干扰的阈红利策略对偶风险的罚金函数,给出了Gerber-Shiu罚金函数的相关结果,由振动引起的罚金函数及由索赔引起的罚金函数满足的微积分方程或更新方程及其解,相应的得出索赔额为指数分布时的破产概率.     

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．     

支付红利的复合二项模型

本文在完全离散的复合二项经典风险模型的基础上,考虑随机地支付红利的模型,当盈余大于或等于一个给定的非负整数红利界,并且没有索赔发生时,保险公司就以概率q0支付一个单位的红利,本文获得了这个模型的破产概率、破产时赤字的分布等的递推公式.     

带借贷利率和门槛分红策略的Erlang(n)盈余过程（英文）

本文考虑带借贷利率和门槛分红策略的Erlang(n)盈余过程:当保险公司的盈余为负数时,允许保险公司以某借贷利率向银行借贷以继续经营业务;当保险公司的盈余超过某个正的门槛值时,保险公司将向其股东支付红利.我们研究了绝对破产时支付红利现值的矩母函数和m阶矩函数.特别地,在Erlang(2)盈余情形下,当索赔额的分布服从指数分布时,我们得到总分红现值的精确解析式;并且利用数值模拟的方法对参数进行了敏感性分析.     

具有延迟索赔风险模型的破产概率

本文考虑一类具有延迟索赔的风险模型,模型中包含两种索赔,其中一种索赔可能延迟发生.在索赔额服从指数分布的情形下,建立此风险模型破产概率所满足的微分方程,得到破产概率的精确表达式,给出了数值模拟结果.     

一类混合分红策略下的广义Erlang(n)风险模型

本文考虑混合分红策略下索赔来到间隔为广义Erlang(n)分布的更新风险模型,利用指数分布的无记忆性,分别得到破产前期望折现分红函数和折现分红的矩母函数满足的积分-微分方程及其边界条件.最后给出索赔为指数分布及索赔来到间隔为广义Erlang(2)分布的风险模型的期望折现分红函数的精确表达式.     

Optimality of the threshold dividend strategy for the compound Poisson model

In this paper, we consider the optimal dividend problem for the compound Poisson risk model. We assume that dividends are paid to the shareholders according to an admissible strategy with dividend rate bounded by a constant. Our objective is to find a dividend policy so as to maximize the expected discounted value of dividends until ruin. We give sufficient conditions under which the optimal strategy is of threshold type.     

Optimal dividends in the Brownian motion risk model with interest

In this paper, we consider a Brownian motion risk model, and in addition, the surplus earns investment income at a constant force of interest. The objective is to find a dividend policy so as to maximize the expected discounted value of dividend payments. It is well known that optimality is achieved by using a barrier strategy for unrestricted dividend rate. However, ultimate ruin of the company is certain if a barrier strategy is applied. In many circumstances this is not desirable. This consideration leads us to impose a restriction on the dividend stream. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. Under this additional constraint, we show that the optimal dividend strategy is formed by a threshold strategy.     

Alternative approach to the optimality of the threshold strategy for spectrally negative Lévy processes

Consider the optimal dividend problem for an insurance company whose uncontrolled surplus precess evolves as a spectrally negative Levy process. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. In this paper, we show that a threshold strategy （also called refraction strategy） forms an optimal strategy under the condition that the Levy measure has a completely monotone density.     

On the Expected Present Value of Total Dividends in a Risk Model with Potentially Delayed Claims

In this paper, we consider a risk model in which two types of individual claims, main claims and by-claims, are defined. Every by-claim is induced by the main claim randomly and may be delayed for one time period with a certain probability. The dividend policy that certain amount of dividends will be paid as long as the surplus is greater than a constant dividend barrier is also introduced into this delayed claims risk model. By means of the probability generating functions, formulae for the expected present value of total dividend payments prior to ruin are obtained for discrete-type individual claims. Explicit expressions for the corresponding results are derived for K n claim amount distributions. Numerical illustrations are also given.     

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.     

Moments of discounted dividend payments in a risk model with randomized dividend-decision times

We consider a perturbed compound Poisson risk model with randomized dividend-decision times. Different from the classical barrier dividend strategy, the insurance company makes decision on whether or not paying off dividends at some discrete time points (called dividend-decision times). Assume that at each dividend-decision time, if the surplus is larger than a barrier b > 0; the excess value will be paid off as dividends. Under such a dividend strategy, we study how to compute the moments of the total discounted dividend payments paid off before ruin.     

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In this paper, we study the dividend problems for finite time interval in the classical risk model. Assume that the dividends are paid according to a barrier strategy in the time interval $[0,t]$, i.e., given a nonnegative barrier value $b$, the dividends only can be paid when the surplus exceeds $b$ and the excess is paid as dividend. Applying the ``differential argument', the equation for the total expected discounted dividends in the time interval $[0,t]$ ($V(x;t)$) is derived, and the explicit expression for the Laplace transform of $V(x;t)$ with respect to $t$ is obtained under the assumption that the claim sizes are exponentially distributed. Finally, a numerical example is given by Stehfest method.     

Dividend problems in the dual model with diffusion and exponentially distributed observation time

Consider dividend problems in the dual model with diffusion and exponentially distributed observation time where dividends are paid according to a barrier strategy. Assume that dividends can only be paid with a certain probability at each point of time, that is, on each observation, if the surplus exceeds the barrier, the excess is paid as dividend. In this paper, integro-differential equations for the expected discounted sum of dividends paid until ruin and the Laplace transform of ruin time are derived. When the gains are exponentially distributed, explicit expressions for the ruin probability, the expected discounted sum of dividends paid until ruin, the Laplace transform of ruin time and the expectation of ruin time are also obtained.     

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.