共查询到20条相似文献,搜索用时 93 毫秒
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《中国科学:数学》2015,(10)
本文对扩散模型下的最优分红问题作了进一步分析.注意到,累积分红量是一个关于时间的右连左极过程,它的路径由连续和跳跃两部分组成.因此,本文在建模中同时加入了连续分红和脉冲分红两种形式,这就构成了一个正则和脉冲分红混合的最优控制问题.假设所有分红量存在一个比例成本,对于每次的脉冲分红量存在一个固定成本.此外,对于连续分红部分,假设存在一个有限的最大分红率.用漂移Brown运动描述公司的盈余过程,优化目标设定为最大化公司破产前分红现值的期望值,本文给出了值函数以及最优分红策略的解析表达式.结论表明,最优的分红策略为阀值(threshold)策略和脉冲策略的组合形式. 相似文献
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本文研究了具有某混合指数索赔分布的经典复合泊松风险模型中的分红问题.利用随机控制理论,在无界分红强度的假设下,给出了值函数的显式表达式和相应的最优分红策略.推广了文献[4]的结果. 相似文献
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本文研究了复合Poisson模型带投资-借贷利率和固定交易费用的最优分红问题。通过控制分红时刻和分红量,最大化直到绝对破产时刻的累积期望折现分红。由于考虑固定交易费用,问题为一个随机脉冲控制问题。首先,本文给出了一个策略是平稳马氏策略的充分必要条件。借助于测度值生成元理论得到测度值动态规划方程(简称测度值DPE),并且在没有任何附加条件下证明了验证定理。通过Lebesgue分解,本文讨论了测度值DPE和拟变分不等式(简称QVI)之间的关系,证明了最优分红策略为具有波段结构的平稳马氏策略。最后,本文给出了求解n-波段策略和相应值函数的算法。当索赔额服从指数分布时,得到了值函数的显示解和最优分红策略。 相似文献
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本文考虑经典风险模型在障碍分红策略下的最优分红值的估计问题.当个体索赔额是混合指数分布时,给出最优分红值的解析表达式.但当个体索赔额是一般分布时,最优分红值的解析表达式往往不能得到,这时我们提供了两种估计方法,一是Lundberg渐近估计法,二是离散化模型估计法.最后给出几个数值例子,对不同计算方法下的估计值作出比较. 相似文献
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In this paper, we consider the Gerber-Shiu expected discounted penalty function for the perturbed compound Poisson risk process with constant force of interest. We decompose the Gerber-Shiu function into two parts: the expected discounted penalty at ruin that is caused by a claim and the expected discounted penalty at ruin due to oscillation. We derive the integral equations and the integro-differential equations for them. By solving the integro-differential equations we get some closed form expressions for the expected discounted penalty functions under certain assumptions. 相似文献
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David Landriault 《Insurance: Mathematics and Economics》2008,42(1):31-38
The risk model with interclaim-dependent claim sizes proposed by Boudreault et al. [Boudreault, M., Cossette, H., Landriault, D., Marceau, E., 2006. On a risk model with dependence between interclaim arrivals and claim sizes. Scand. Actur. J., 265-285] is studied in the presence of a constant dividend barrier. An integro-differential equation for some Gerber-Shiu discounted penalty functions is derived. We show that its solution can be expressed as the solution to the Gerber-Shiu discounted penalty function in the same risk model with the absence of a barrier and a combination of two linearly independent solutions to the associated homogeneous integro-differential equation. Finally, we analyze the expected present value of dividend payments before ruin in the same class of risk models. An homogeneous integro-differential equation is derived and then solved. Its solution can be expressed as a different combination of the two fundamental solutions to the homogeneous integro-differential equation associated to the Gerber-Shiu discounted penalty function. 相似文献
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The main focus of this paper is to analyze the Gerber-Shiu penalty function of a compound Poisson risk model with delayed claims and random incomes. It is assumed that every main claim will produce a by-claim which can be delayed with a certain probability. We derive the integral equation satisfied by the Gerber-Shiu penalty function. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the Gerber-Shiu penalty function is derived. Finally, when the premium sizes have rational Laplace transforms, we also obtain the Laplace transform of the Gerber-Shiu penalty function. 相似文献
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In this paper, the discounted penalty (Gerber-Shiu) functions for a risk model involving two independent classes of insurance risks under a threshold dividend strategy are developed. We also assume that the two claim number processes are independent Poisson and generalized Erlang (2) processes, respectively. When the surplus is above this threshold level, dividends are paid at a constant rate that does not exceed the premium rate. Two systems of integro-differential equations for discounted penalty functions are derived, based on whether the surplus is above this threshold level. Laplace transformations of the discounted penalty functions when the surplus is below the threshold level are obtained. And we also derive a system of renewal equations satisfied by the discounted penalty function with initial surplus above the threshold strategy via the Dickson-Hipp operator. Finally, analytical solutions of the two systems of integro-differential equations are presented. 相似文献
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In this paper, a risk model where claims arrive according to a Markovian arrival process (MAP) is considered. A generalization of the well-known Gerber-Shiu function is proposed by incorporating the maximum surplus level before ruin into the penalty function. For this wider class of penalty functions, we show that the generalized Gerber-Shiu function can be expressed in terms of the original Gerber-Shiu function (see e.g. [Gerber, Hans U., Shiu, Elias, S.W., 1998. On the time value of ruin. North American Actuarial Journal 2(1), 48-72]) and the Laplace transform of a first passage time which are both readily available. The generalized Gerber-Shiu function is also shown to be closely related to the original Gerber-Shiu function in the same MAP risk model subject to a dividend barrier strategy. The simplest case of a MAP risk model, namely the classical compound Poisson risk model, will be studied in more detail. In particular, the discounted joint density of the surplus prior to ruin, the deficit at ruin and the maximum surplus before ruin is obtained through analytic Laplace transform inversion of a specific generalized Gerber-Shiu function. Numerical illustrations are then examined. 相似文献
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The Gerber-Shiu discounted penalty function in the risk process with phase-type interclaim times 总被引:1,自引:0,他引:1
In this paper, we consider the Gerber-Shiu discounted penalty function for the Sparre Anderson risk process in which the interclaim times have a phase-type distribution. By the Markov property of a joint process composed of the risk process and the underlying Markov process, we provide a new approach to prove the systems of integro-differential equations for the Gerber-Shiu functions. Closed form expressions for the Gerber-Shiu functions are obtained when the claim amount distribution is from the rational family. Finally we compute several numerical examples intended to illustrate the main results. 相似文献
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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. 相似文献
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In this paper, we investigate the Gerber-Shiu discounted penalty function for the surplus process described by a piecewise deterministic Markov process (PDMP). We derive an integral equation for the Gerber-Shiu discounted penalty function, and obtain the exact solution when the initial surplus is zero. Dickson formulae are also generalized to the present surplus process. 相似文献