共查询到20条相似文献,搜索用时 62 毫秒
1.
Yang Yang Remigijus Leipus Jonas Šiaulys Yuquan Cang 《Journal of Mathematical Analysis and Applications》2011,383(1):215-225
This paper investigates the finite-time ruin probability in the dependent renewal risk model, where the claim sizes are independent and identically distributed random variables with strongly subexponential tails, and the interarrival times are negatively dependent. We establish an asymptotic estimate, which holds uniformly for the time horizon varying in the positive half line. 相似文献
2.
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
3.
研究了亚指数分布族中一类特殊的分布,在年索赔额服从该特殊分布的假设下,推导出了的终极破产概率的渐进表达式,提出了可以用随机模拟方法对于服从亚指数分布的破产概率进行模拟计算的方法.从实践的角度来说,更具有可操作性,为保险业提供了一些应对极值概率事件的理论依据和检验方法. 相似文献
4.
This paper considers a bidimensional renewal risk model with constant interest force and dependent subexponential claims. Under the assumption that the claim size vectors form a sequence of independent and identically distributed random vectors following a common bivariate Farlie–Gumbel–Morgenstern distribution, we derive for the finite-time ruin probability an explicit asymptotic formula. 相似文献
5.
The authors investigate the tail probability of the supremum of a random walk with independent increments and obtain some equivalent assertions in the case that the increments are independent and identically distributed random variables with O-subexponential integrated distributions. A uniform upper bound is derived for the distribution of the supremum of a random walk with independent but non-identically distributed increments, whose tail distributions are dominated by a common tail distribution with an O-subexponential integrated distribution. 相似文献
6.
Consider a discrete-time risk model with insurance and financial risks in a stochastic economic environment. Assume that the insurance and financial risks form a sequence of independent and identically distributed random vectors with a generic random vector following a wide type of dependence structure. An asymptotic formula for the finite-time ruin probability with subexponential insurance risks is derived. In doing so, the subexponentiality of the product of two dependent random variables is investigated simultaneously. 相似文献
7.
This paper considers the asymptotics of randomly weighted sums and their maxima, where the increments {X_i,i\geq1\} is a sequence of independent, identically distributed and real-valued random variables and the weights {\theta_i,i\geq1\} form another sequence of non-negative and independent random variables, and the two sequences of random variables follow some dependence structures. When the common distribution F of the increments belongs to dominant variation class, we obtain some weakly asymptotic estimations for the tail probability of randomly weighted sums and their maxima. In particular, when the F
belongs to consistent variation class, some asymptotic formulas is presented. Finally, these results are applied to the asymptotic estimation for the ruin probability. 相似文献
8.
Dominik Kortschak Hansjörg Albrecher 《Methodology and Computing in Applied Probability》2009,11(3):279-306
In this paper we extend some results about the probability that the sum of n dependent subexponential random variables exceeds a given threshold u. In particular, the case of non-identically distributed and not necessarily positive random variables is investigated. Furthermore
we establish criteria how far the tail of the marginal distribution of an individual summand may deviate from the others so
that it still influences the asymptotic behavior of the sum. Finally we explicitly construct a dependence structure for which,
even for regularly varying marginal distributions, no asymptotic limit of the tail of the sum exists. Some explicit calculations
for diagonal copulas and t-copulas are given.
Dominik Kortschak was supported by the Austrian Science Fund Project P18392. 相似文献
9.
Grzegorz Guzik 《随机分析与应用》2016,34(1):24-37
We consider a Markov chain generated by random iterations of a family of mappings indexed by elements of an arbitrary measurable space. Under sufficiently weak assumptions we construct a family of place-dependent probability measures such that considered Markov chain converges to a stationary distribution. We also prove some sufficient condition for asymptotic stability of a family of i.i.d. mappings and we apply obtained result for discrete white noise random dynamical systems showing analogous probabilistic long-time behavior. 相似文献
10.
In this paper we study the asymptotic behavior of the tail probabilities of sums of dependent and real-valued random variables
whose distributions are assumed to be subexponential and not necessarily of dominated variation. We propose two general dependence
assumptions under which the asymptotic behavior of the tail probabilities of the sums is the same as that in the independent
case. In particular, the two dependence assumptions are satisfied by multivariate Farlie-Gumbel-Morgenstern distributions. 相似文献
11.
B. S. Choi 《Annals of the Institute of Statistical Mathematics》1985,37(1):535-539
Summary It is shown that a normal probability density can be characterized as a limit of conditional probability densities of i.i.d.
uniform random variables. 相似文献
12.
We consider the classical M/G/1 queue with two priority classes and the nonpreemptive and preemptive-resume disciplines. We show that the low-priority steady-state
waiting-time can be expressed as a geometric random sum of i.i.d. random variables, just like the M/G/1 FIFO waiting-time distribution. We exploit this structures to determine the asymptotic behavior of the tail probabilities.
Unlike the FIFO case, there is routinely a region of the parameters such that the tail probabilities have non-exponential
asymptotics. This phenomenon even occurs when both service-time distributions are exponential. When non-exponential asymptotics
holds, the asymptotic form tends to be determined by the non-exponential asymptotics for the high-priority busy-period distribution.
We obtain asymptotic expansions for the low-priority waiting-time distribution by obtaining an asymptotic expansion for the
busy-period transform from Kendall's functional equation. We identify the boundary between the exponential and non-exponential
asymptotic regions. For the special cases of an exponential high-priority service-time distribution and of common general
service-time distributions, we obtain convenient explicit forms for the low-priority waiting-time transform. We also establish
asymptotic results for cases with long-tail service-time distributions. As with FIFO, the exponential asymptotics tend to
provide excellent approximations, while the non-exponential asymptotics do not, but the asymptotic relations indicate the
general form. In all cases, exact results can be obtained by numerically inverting the waiting-time transform.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
13.
Hai-zhong Yang 《应用数学学报(英文版)》2011,27(2):277-280
This paper investigates the asymptotic behavior of tail probability of randomly weighted sums of dependent and real-valued
random variables with dominated variation, where the weights form another sequence of nonnegative random variables. The result
we obtain extends the corresponding result of Wang and Tang[7]. 相似文献
14.
Inés Armendáriz 《Stochastic Processes and their Applications》2011,121(5):1138-1147
It is known that large deviations of sums of subexponential random variables are most likely realised by deviations of a single random variable. In this article we give a detailed picture of how subexponential random variables are distributed when a large deviation of the sum is observed. 相似文献
15.
Fengyang CHENG 《数学年刊B辑(英文版)》2020,41(3):441-450
The author obtains that the asymptotic relations ■ hold as x→∞, where the random weights θ1,···, θn are bounded away both from 0 and from∞with no dependency assumptions, independent of the primary random variables X1,···, Xn which have a certain kind of dependence structure and follow non-identically subexponential distributions. In particular, the asymptotic relations remain true when X1,···, Xn jointly follow a pairwise Sarmanov... 相似文献
16.
Jiangyan Peng 《Stochastics An International Journal of Probability and Stochastic Processes》2018,90(3):432-471
In this paper, an insurer is allowed to make risk-free and risky investments, and the price process of the investment portfolio is described as an exponential Lévy process. We study the asymptotic tail behavior for a non-standard renewal risk model with dependence structures. The claim sizes are assumed to follow a one-sided linear process with independent and identically distributed step sizes, and the step sizes and inter-arrival times form a sequence of independent and identically distributed random pairs with a dependence structure. When the step-size distribution is heavy tailed, we obtain some uniform asymptotics for the finite-and infinite-time ruin probabilities. 相似文献
17.
We consider a nonstandard risk model with constant interest rate. For the case where the claim sizes follow a common heavy-tailed
distribution and fulfill a dependence structure proposed by Geluk and Tang [J. Geluk and Q. Tang, Asymptotic tail probabilities
of sums of dependent subexponential random variables, J. Theor. Probab., 22:871–882, 2009] while the interarrival times fulfill the so-called widely lower orthant dependence, we establish a weakly
asymptotically equivalent formula for the infinite-time ruin probability. In particular, when the dependence structure for
claim sizes is strengthened to the widely upper orthant dependence, this result implies a uniformly asymptotically equivalent
formula for the finite-time and infinite-time ruin probabilities. 相似文献
18.
We study the asymptotic behavior of the tail probabilities of the waiting time and the busy period for the $M/G/1/K$ queues with subexponential service times under three different service disciplines: FCFS, LCFS, and ROS. Under the FCFS discipline, the result on the waiting time is proved for the more general $GI/G/1/K$ queue with subexponential service times and lighter interarrival times. Using the well-known Laplace–Stieltjes transform (LST) expressions for the probability distribution of the busy period of the $M/G/1/K$ queue, we decompose the busy period into a sum of a random number of independent random variables. The result is used to obtain the tail asymptotics for the waiting time distributions under the LCFS and ROS disciplines. 相似文献
19.
唐启鹤 《中国科学A辑(英文版)》2002,45(5):632-639
The famous Embrechts-Goldie-Veraverbeke formula shows that, in the classical Cramér-Lundberg risk model, the ruin probabilities satisfy \(R(x, \infty ) \sim \rho ^{ - 1} \bar F_e (x)\) if the claim sizes are heavy-tailed, where Fe denotes the equilibrium distribution of the common d.f. F of the i.i.d. claims, ? is the safety loading coefficient of the model and the limit process is for x → ∞. In this paper we obtain a related local asymptotic relationship for the ruin probabilities. In doing this we establish two lemmas regarding the n-fold convolution of subexponential equilibrium distributions, which are of significance on their own right. 相似文献
20.
We derive upper and lower bounds for the ruin probability over infinite time in the classical actuarial risk model (usual independence and equidistribution assumptions; the claim-number process is Poisson). Our starting point is the renewal equation for the ruin probability, but no renewal theory is used, except for the elementary facts proved in the note. Some bounds allow a very simple new proof of an asymptotic result akin to heavy-tailed claim-size distributions. 相似文献