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本文考虑了带多阈值两类索赔到达风险模型,在假定两类索赔到达过程均为phase-type 分布时,建立了期望折现罚函数所满足的积分-微分方程.并通过拉普拉斯变换讨论了方程的解. 相似文献
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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. 相似文献
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本文在经典风险模型的基础上,将索赔到达过程推广为更新过程,索赔可以批量到达,且带有常数利息力和Brown运动干扰项,得到一个新的风险模型,运用Markov骨架过程的方法,得出盈余过程的瞬时分布和生存概率. 相似文献
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本文考虑了索赔时间间距为phase-type分布时带干扰更新风险模型中的破产前最大盈余、破产后赤字的分布,建立了相应的积分-微分方程.最后,讨论了当索赔时间间距为Erlang(2)分布且索赔量满足指数分布时的特殊情形. 相似文献
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本文考虑索赔次数到达过程是一类Cox过程的风险模型中的Gerber-shiu平均折现罚函数,建立该函数所满足的积分-微分方程,得出两状态下索赔量分布函数属于K_n-类时破产时间函数的具体表达式. 相似文献
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本文研究了一类特殊的更新风险过程,其索赔时间间隔服从混合指数分布.首先,建立保险公司在时刻t的资产盈余模型,然后在该模型的基础上,根据Gerber的积分微分方程法和Laplace变换计算该公司的生存概率和赤字分布,最后分析盈余过程能顺利达到某一水平而不发生破产的概率. 相似文献
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重尾索赔下的一类相依风险模型的若干问题 总被引:2,自引:2,他引:0
本文研究了重尾索赔下的一类相依风险模型,得到了破产概率的尾等价式及索赔盈余过程大偏差的渐近关系式.在该模型中,一索赔到达过程是Poisson过程,另一索赔到达过程为其p-稀疏过程. 相似文献
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高珊 《数学的实践与认识》2008,38(22)
研究了一类相依的双险种风险模型,其中第一类险种的索赔到达计数过程为E lang(2)过程,第二类险种的索赔到达计数过程为其p-稀疏过程.首先通过更新论证的方法得到罚金折现期望满足的积分-微分方程,然后推导拉普拉斯变换的表达式,并就索赔额服从指数分布的情形得到了罚金折现期望的精确表达式. 相似文献
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Dividend payments with a threshold strategy in the compound Poisson risk model perturbed by diffusion 总被引:2,自引:0,他引:2
In the absence of dividends, the surplus of an insurance company is modelled by a compound Poisson process perturbed by diffusion. Dividends are paid at a constant rate whenever the modified surplus is above the threshold, otherwise no dividends are paid. Two integro-differential equations for the expected discounted dividend payments prior to ruin are derived and closed-form solutions are given. Accordingly, the Gerber–Shiu expected discounted penalty function and some ruin related functionals, the probability of ultimate ruin, the time of ruin and the surplus before ruin and the deficit at ruin, are considered and their analytic expressions are given by general solution formulas. Finally the moment-generating function of the total discounted dividends until ruin is discussed. 相似文献
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本文对索赔次数为复合Poisson-Geometric过程的风险模型,在保险公司的盈余可以投资于风险资产,以及索赔购买比例再保险的策略下,研究使得破产概率最小的最优投资和再保险策略.通过求解相应的Hamilton-Jacobi-Bellman方程,得到使得破产概率最小的最优投资和比例再保险策略,以及最小破产概率的显示表达式. 相似文献
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We consider the threshold dividend strategy where a company’s surplus process is described by the dual Lévy risk model. Namely, the company chooses to pay dividends at a constant rate only when the surplus is above some nonnegative threshold. Classically, such a company is referred to be ruined immediately when the surplus level becomes negative. Recently, researchers investigate the Parisian ruin problem where the company is allowed to operate under negative surplus for a predetermined period known as the Parisian delay. With the help of the fluctuation identities of spectrally negative Lévy processes, we obtain an explicit expression of the expected discounted dividends until Parisian ruin in terms of the relevant scale functions and certain probabilities that need to be evaluated for each specific Lévy process. The optimal threshold level under such a threshold dividend strategy is deduced. Applications and numerical examples are given to illustrate the theoretical results and examine how the expected discounted aggregate dividends and the optimal threshold level change in response to different Parisian delays. 相似文献
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This paper considers a robust optimal investment and reinsurance problem with multiple dependent risks for an Ambiguity-Averse Insurer (AAI), who is uncertain about the model parameters. We assume that the surplus of the insurance company can be allocated to the financial market consisting of one risk-free asset and one risky asset whose price process satisfies square root factor process. Under the objective of maximizing the expected utility of the terminal surplus, by adopting the technique of stochastic control, closed-form expressions of the robust optimal strategy and the corresponding value function are derived. The verification theorem is also provided. Finally, by presenting some numerical examples, the impact of some parameters on the optimal strategy is illustrated and some economic explanations are also given. We find that the robust optimal reinsurance strategies under the generalized mean–variance premium are very different from that under the variance premium principle. In addition, ignoring model uncertainty risk will lead to significant utility loss for the AAI. 相似文献
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利润最大化风险最小化是保险公司运营所追求的目标,破产概率为公司进行风险决策提供了依据。本文基于随机利率环境下,保费随公司盈余水平调整的双分红复合帕斯卡模型,研究了股份制保险公司的有限时间破产概率。我们证明了公司盈余过程的齐次马氏性,得到了有限时间破产概率的计算方法,最后给出了具体算例。 相似文献
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We consider the Omega model with underlying Ornstein-Uhlenbeck type surplus process for an insurance company and obtain some useful results. Explicit expressions for the expected discounted penalty function at bankruptcy with a constant bankruptcy rate and linear bankruptcy rate are derived. Based on random observations of the surplus process, we examine the differentiability for the expected discounted penalty function at bankruptcy especially at zero. Finally, we give the Laplace transforms for occupation times as an important example of Li and Zhou [Adv. Appl. Probab., 2013, 45(4): 1049–1067]. 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, we assume that the surplus process of an insurance entity is represented by a pure diffusion. The company can invest its surplus into a Black-Scholes risky asset and a risk free asset. We impose investment restrictions that only a limited amount is allowed in the risky asset and that no short-selling is allowed. We further assume that when the surplus level becomes negative, the company can borrow to continue financing. The ultimate objective is to seek an optimal investment strategy that minimizes the probability of absolute ruin, i.e. the probability that the liminf of the surplus process is negative infinity. The corresponding Hamilton-Jacobi-Bellman (HJB) equation is analyzed and a verification theorem is proved; applying the HJB method we obtain explicit expressions for the S-shaped minimal absolute ruin function and its associated optimal investment strategy. In the second part of the paper, we study the optimization problem with both investment and proportional reinsurance control. There the minimal absolute ruin function and the feedback optimal investment-reinsurance control are found explicitly as well. 相似文献