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1.
《Mathematical Methods in the Applied Sciences》2018,41(10):3820-3831
In this article, we consider the problem of finding the ultimate ruin probability in the classical risk mode. Using Laplace transform inversion and Fourier transform, we obtain ultimate ruin probability of an insurance company. First, we show that this problem is ill‐posed in the sense of Hadamard. Then, we apply the Tikhonov and truncation methods for establishing the approximate function for the ultimate ruin probability. Furthermore, convergence of the method, together with some examples, will be given. Finally, we present a numerical example to show efficiency of the method. 相似文献
2.
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
3.
In this paper the well-known insurance ruin problem is reconsidered. The ruin probability is estimated in the case of an unknown
claims density, assuming a sample of claims is given. An important step in the construction of the estimator is the application
of a regularized version of the inverse of the Laplace transform. A rate of convergence in probability for the integrated
squared error (ISE) is derived and a simulation study is included.
相似文献
4.
Traditionally, an insurance risk process describes an insurance company’s risk through some criteria using the historical data under the framework of probability theory with the prerequisite that the estimated distribution function is close enough to the true frequency. However, because of the complexity and changeability of the world, economical and technological reasons in many cases enough historical data are unavailable and we have to base on belief degrees given by some domain experts, which motivates us to include the human uncertainty in the insurance risk process by regarding interarrival times and claim amounts as uncertain variables using uncertainty theory. Noting the expansion of insurance companies’ operation scale and the increase of businesses with different risk nature, in this paper we extend the uncertain insurance risk process with a single class of claims to that with multiple classes of claims, and derive expressions for the ruin index and the uncertainty distribution of ruin time respectively. As the ruin time can be infinite, we propose a proper uncertain variable and the corresponding proper uncertainty distribution of that. Some numerical examples are documented to illustrate our results. Finally our method is applied to a real-world problem with some satellite insurance data provided by global insurance brokerage MARSH. 相似文献
5.
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
6.
Jinzhu Li 《Journal of Mathematical Analysis and Applications》2012,387(2):1009-1023
In this paper we study the asymptotic tail behavior for a non-standard renewal risk model with a dependence structure and stochastic return. An insurance company is allowed to invest in financial assets such as risk-free bonds and risky stocks, and the price process of its portfolio is described by a geometric Lévy process. By restricting the claim-size distribution to the class of extended regular variation (ERV) and imposing a constraint on the Lévy process in terms of its Laplace exponent, we obtain for the tail probability of the stochastic present value of aggregate claims a precise asymptotic formula, which holds uniformly for all time horizons. We further prove that the corresponding ruin probability also satisfies the same asymptotic formula. 相似文献
7.
Dongya Cheng 《Stochastics An International Journal of Probability and Stochastic Processes》2019,91(5):643-656
This paper considers a bidimensional continuous-time renewal risk model of insurance business with different claim-number processes and strongly subexponential claims. For the finite-time ruin probability defined as the probability for the aggregate surplus process to break down the horizontal line at the level zero within a given time, an uniform asymptotic formula is established, which provides new insights into the solvency ability of the insurance company. 相似文献
8.
We study the probability of ruin before time t for the family of tempered stable Lévy insurance risk processes, which includes the spectrally positive inverse Gaussian processes. Numerical approximations of the ruin time distribution are derived via the Laplace transform of the asymptotic ruin time distribution, for which we have an explicit expression. These are benchmarked against simulations based on importance sampling using stable processes. Theoretical consequences of the asymptotic formulae indicate that some care is needed in the choice of parameters to avoid exponential growth (in time) of the ruin probabilities in these models. This, in particular, applies to the inverse Gaussian process when the safety loading is less than one. 相似文献
9.
In this article, we consider the perturbed classical surplus model. We study the probability that ruin occurs at each instant of claims, the probability that ruin occurs between two consecutive claims occurrences, as well as the distribution of the ruin time that lies in between two consecutive claims. We give some finite expressions depending on derivatives for Laplace transforms, which can allow computation of the probabilities concerning with claim occurrences. Further, we present some insight on the shapes of probability functions involved. 相似文献
10.
11.
关于常利率风险模型在破产前后余额的分布 总被引:2,自引:0,他引:2
本文对常利率风险模型运用拉普拉斯变换给出了破产前后余额通过破产概率函数表示的有限公式,以及破产概率的分析表达式,另外对于破产前后余额分布的密度与破产前余额密度之间关系简要说明。 相似文献
12.
研究了当保费率随理赔强度的变化而变化时C ox风险模型的折现罚金函数,利用后向差分法得到了折现罚金函数所满足的积分方程,进而得到了破产概率,破产前瞬时盈余、破产时赤字的各阶矩所满足的积分方程.最后给出当理赔额服从指数分布,理赔强度为两状态的马氏过程时破产概率的拉普拉斯变换,对一些具体数值计算出了破产概率的表达式. 相似文献
13.
We follow some recent works to study the ruin probabilities of a bidimensional perturbed insurance risk model. For the case of light-tailed claims, using the martingale technique we obtain for the infinite-time ruin probability a Lundberg-type upper bound, which captures certain information of dependence between the two marginal surplus processes. For the case of heavy-tailed claims, we derive for the finite-time ruin probability an explicit asymptotic estimate. 相似文献
14.
Sun Chuanguang 《高校应用数学学报(英文版)》2007,22(1):109-118
In this paper a class of risk processes in which claims occur as a renewal process is studied. A clear expression for Laplace transform of the survival probability is well given when the claim amount distribution is Erlang distribution or mixed Erlang distribution. The expressions for moments of the time to ruin with the model above are given. 相似文献
15.
In this paper, we study the joint Laplace transform and probability generating functions of two pairs of random variables: (1) the two-sided first-exit time and the number of claims by this time; (2) the two-sided smooth exit-recovery time and its associated number of claims. The joint transforms are expressed in terms of the so-called doubly-killed scale function that is defined in this paper. We also find explicit expressions for the joint density function of the two-sided first-exit time and the number of claims by this time. Numerical examples are presented for exponential claims. 相似文献
16.
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. 相似文献
17.
In this paper, we investigate a renewal risk model in which the distribution of the interclaim times is a mixture of two Erlang
distributions. First, the Laplace transform and the defective renewal equation for the Gerber-Shiu function are derived. Then,
two asymptotic results for the Laplace transform of the time of ruin are given when the initial surplus tends to infinity
for the light-tailed claims and heavy-tailed claims, respectively. Finally, an explicit expression for the Gerber-Shiu function
is given. 相似文献
18.
We study the problem of evaluation of the probability of ruin of an insurance company for infinitely many steps in the case
where the company can invest its capital to bank deposits at any time. As a distribution of the amounts of claims to the insurance
company, we use the gamma-distribution with the parameters n and α.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 4, pp. 447–457, April, 2007. 相似文献
19.
In this paper, we consider two dependent classes of insurance business with heavy‐tailed claims. The dependence comes from the assumption that claim arrivals of the two classes are governed by a common renewal counting process. We study two types of ruin in the two‐dimensional framework. For each type of ruin, we establish an asymptotic formula for the finite‐time ruin probability. These formulae possess a certain uniformity feature in the time horizon. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
20.
We investigate an insurance risk model that consists of two reserves which receive income at fixed rates. Claims are being requested at random epochs from each reserve and the interclaim times are generally distributed. The two reserves are coupled in the sense that at a claim arrival epoch, claims are being requested from both reserves and the amounts requested are correlated. In addition, the claim amounts are correlated with the time elapsed since the previous claim arrival.We focus on the probability that this bivariate reserve process survives indefinitely. The infinite-horizon survival problem is shown to be related to the problem of determining the equilibrium distribution of a random walk with vector-valued increments with ‘reflecting’ boundary. This reflected random walk is actually the waiting time process in a queueing system dual to the bivariate ruin process.Under assumptions on the arrival process and the claim amounts, and using Wiener–Hopf factorization with one parameter, we explicitly determine the Laplace–Stieltjes transform of the survival function, c.q., the two-dimensional equilibrium waiting time distribution.Finally, the bivariate transforms are evaluated for some examples, including for proportional reinsurance, and the bivariate ruin functions are numerically calculated using an efficient inversion scheme. 相似文献