Dividend payments in the perturbed compound poisson risk model with liquid reserve and interest

考虑一类资产盈余具有流动储备金和利率的带干扰的复合泊松风险模型的分红问题,得到了累积分红现值的矩母函数,n阶原点矩所满足的积分-微分方程及边界条件,并给出了索赔额为指数分布时相应积分-微分方程解的具体表达式.     

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.     

常利率和门限分红策略下带干扰的泊松风险模型的绝对破产问题

本文考虑常利率和门限分红策略下带干扰的泊松风险模型的绝对破产问题,得到了累积分红现值的矩母函数, n阶原点矩所满足的积分-微分方程及边界条件;进一步得到了此模型下Gerber-Shiu折现罚函数所满足的积分-微分方程及相应边界条件,相应地将其转化为Volterra型积分方程,最后给出了索赔额为指数分布时绝对破产概率的解析表达式.     

阈值分红策略下带常利率的对偶风险模型

研究了常利率下基于对偶复合泊松模型带阈值的分红策略,给出了公司在破产时累积红利期望现值函数的两个积分-微分方程,分情况讨论了收益服从指数分布时的显示表达式,以及服从一般分布时的拉普拉斯变换表达式.     

常数分红界下两离散相依险种风险模型的分红问题

主要研究了常数分红界下两离散相依险种风险模型的分红问题.模型假定一个险种的主索赔以一定的概率引起另外一险种的副索赔,且副索赔可能延迟发生,推导了到破产前一时刻为止累积分红折现均值满足的差分方程,并得到了特殊索赔额下累积分红折现均值的具体表达式,最后结合实际例子进行了数值模拟.     

一类索赔相依二元风险模型的破产概率问题研究

考虑一种相依索赔风险模型,模型中假设每次主索赔可随机产生一延迟的副索赔,采用Laplacc变换方法,给出了索赔额服从轻尾分布时的最终破产概率,并研究了重尾分布时最终破产概率的渐进式.     

生存概率控制下的周期性红利优化问题

文章主要在带有利息收益的离散时间盈余模型中,在生存概率和有界红利率的约束条件下,讨论周期性红利优化问题:最大化破产前累积的周期性支付的红利现值的期望,并获得最优红利策略.假设在每个单位时间内收到的保费是正实值随机变量,且保费序列构成一个马尔科夫链.此外,我们还假设任意单位时间内索赔发生的概率和相应单位时间内收到的保费相关.首先,给定生存概率的约束条件,得到了红利支付的约束门槛.然后,通过变换值函数和运用不动点原理,得到了最优红利策略的一些性质和算法.最后通过数值实例解释该算法,并讨论生存概率对最优红利策略的影响.数值结果显示,最优红利策略是一个条件多门槛策略.这为现代企业(尤其是保险和金融公司)的决策者在兼顾和平衡公司健康发展与股东利益而进行红利决策和定量分析时提供了理论依据.     

具有分红、流动储备金和利率的风险模型的绝对破产

建立了阈值分红策略下具有流动储备金、投资利率和贷款利率的复合泊松风险模型.利用全概率公式和泰勒展式,推导出了该模型的Gerber-Shiu函数和绝对破产时刻的累积分红现值期望满足的积分-微分方程及边界条件,借助Volterra方程,给出了Gerber-Shiu函数的解析表达式.     

具有常红利边界和延迟索赔的一类离散更新风险模型

考虑了具有常红利边界和延迟索赔的一类离散更新风险模型,其中间隔索赔到达时间从离散phase-type分布.定义了两种类型的索赔:主索赔和副索赔,主索赔以一定的概率引起副索赔且副索赔会以一定的概率被延迟到下一时段.通过引入辅助风险模型,推导了破产前红利折现期望满足的差分方程及其解.最后给出了当索赔额服从几何分布时的有关数值例子.     

离散的相依风险模型的破产问题

研究一类索赔时间相依的离散风险模型,模型中假设每次主索赔可能引起一次副索赔,而每次副索赔有可能延迟发生.通过引入辅助模型,运用概率论的分析方法得到了破产前瞬时盈余和破产时赤字联合分布的递推解,以及初始值为0时最终破产概率的明确表达式.最后结合保险实例进行了数值模拟.     

Expected present value of total dividends in a delayed claims risk model under stochastic interest rates

In this paper, a compound binomial risk model with a constant dividend barrier under stochastic interest rates is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. In the evaluation of the expected present value of dividends, the interest rates are assumed to follow a Markov chain with finite state space. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are K_n distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.     

有限状态多期模型下的最小熵等价鞅测度及其应用

采用有限状态多期模型描述股票价格变动过程,导出了有红利支付情形下的最小熵等价鞅测度,给出了股票价格变动趋势的风险中性预期与红利率和无风险利率之间相对大小的关系,从理论上证明了无风险利率大于股票红利率时,市场将呈现出一种向上的风险中性趋势;无风险利率小于股票红利率时,市场将呈现出一种向下的风险中性趋势;无风险利率等于红利率时,股票价格将围绕初始价格上下波动而没有明显的风险中性趋势.     

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．     

An elementary approach to discrete models of dividend strategies

The paper studies a discrete counterpart of Gerber et al. (2006). The surplus of an insurance company (before dividends) is modeled as a time-homogeneous Markov chain with possible changes of size +1,0,−1,−2,−3,…. If a barrier strategy is applied for paying dividends, it is shown that the dividends-penalty identity holds. The identity expresses the expected present value of a penalty at ruin in terms of the expected discounted dividends until ruin and the expected present value of the penalty at ruin if no dividends are paid. For the problem of maximizing the difference between the expected discounted dividends until ruin and the expected present value of the penalty at ruin, barrier strategies play a prominent role. In some cases an optimal dividend barrier exists. The paper discusses in detail the special case where the distribution of the change in surplus does not depend on the current surplus (so that in the absence of dividends the surplus process has independent increments). A closed-form result for zero initial surplus is given, and it is shown how the relevant quantities can be calculated recursively. Finally, it is shown how optimal dividend strategies can be determined; typically, they are band strategies.     

Optimal dividend strategy in compound binomial model with bounded dividend rates

We consider the compound binomial model, and assume that dividends are paid to the shareholders according to an admissible strategy with dividend rates bounded by a constant.The company controls the amount of dividends in order to maximize the cumulative expected discounted dividends prior to ruin. We show that the optimal value function is the unique solution of a discrete HJB equation. Moreover, we obtain some properties of the optimal payment strategy, and offer a simple algorithm for obtaining the optimal strategy. The key of our method is to transform the value function. Numerical examples are presented to illustrate the transformation method.     

On the total operating costs up to default in a renewal risk model

The paper proposes a new approach to study a general class of ruin-related quantities in the context of a renewal risk model. While the classical approaches in Sparre Andersen models have their own merits, the approach presented in this paper has its advantages from the following perspectives. (1) The underlying surplus process has the flexibility to reflect a broad range of scenarios for surplus growth including dividend policies and interest returns. (2) The solution method provides a general framework to unify a great variety of existing ruin-related quantities such as Gerber–Shiu functions and the expected present value of dividends paid up to ruin, and facilitates derivations of new ruin-related quantities such as the expected present value of total claim costs up to ruin, etc. In the end, many specific examples are explored to demonstrate its application in renewal risk models.     

Optimal financing and dividend control of the insurance company with excess-of-loss reinsurance policy

In this paper, we consider an optimal financing and dividend control problem of an insurance company. The management of the insurance company controls the dividends payout, equity issuance and the excess-of-loss reinsurance policy. In our model, the dividends are assumed to be paid out continuously, which is of interest from the perspective of financial modeling. The objective is to find the strategy which maximizes the expected present values of the dividends payout minus the equity issuance up to the time of ruin. We solve the optimal control problem and identify the optimal strategy by constructing two categories of suboptimal control problems.     

Optimal choice of dividend barriers for a risk process with stochastic return on investments

We consider a risk process with stochastic return on investments and we are interested in expected present value of all dividends paid until ruin occurs when the company uses a simple barrier strategy, i.e. when it pays dividends whenever its surplus reaches a level b. It is shown that given the barrier b, this expected value can be found by solving a boundary value problem for an integro-differential equation. The solution is then found in two special cases; when return on investments is constant and the surplus generating process is compound Poisson with exponentially distributed claims, and also when both return on investments as well as the surplus generating process are Brownian motions with drift. Also in this latter case we are able to find the optimal barrier b^*, i.e. the barrier that gives the highest expected present value of dividends. Parallell with this we treat the problem of finding the Laplace transform of the distribution of the time to ruin when a barrier strategy is employed, noting that the probability of eventual ruin is 1 in this case. The paper ends with a short discussion of the same problems when a time dependent barrier is employed.     

马氏相依风险模型红利折现的矩

该文讨论常数红利边界下的马氏相依模型的矩的问题. 首先, 推导出破产前全部红利的折现期望、红利折现的高阶矩所满足的积分-微分方程组及相应的边界条件. 然后, 通过构造特殊的初始条件, 利用Laplace变换, 在给定的一类索赔分布下, 得到上面方程组的显式解. 最后, 给出两状态下指数索赔的数值计算结果.