Ruin probability and joint distributions of some actuarial random vectors in the compound pascal model

The compound negative binomial model,introduced in this paper,is a discrete time version.We discuss the Markov properties of the surplus process,and study the ruin probability and the joint distributions of actuarial random vectors in this model.By the strong Markov property and the mass function of a defective renewal sequence,we obtain the explicit expressions of the ruin probability,the finite-horizon ruin probability,the joint distributions of T,U(T-1),|U(T)| and 0≤inn相似文献   

A Class of Ruin Probability Mo del with Dep endent Structure

In this paper, we study a class of ruin problems, in which premiums and claims are dependent. Under the assumption that premium income is a stochastic process, we raise the model that premiums and claims are dependent, give its numerical characteristics and the ruin probability of the individual risk model in the surplus process. In addition, we promote the number of insurance policies to a Poisson process with parameter λ, using martingale methods to obtain the upper bound of the ultimate ruin probability.     

Ruin probabilities for a risk model with two classes of claims

In this paper we consider a risk model with two kinds of claims, whose claims number processes are Poisson process and ordinary renewal process respectively. For this model, the surplus process is not Markovian, however, it can be Markovianized by introducing a supplementary process, We prove the Markov property of the related vector processes. Because such obtained processes belong to the class of the so-called piecewise-deterministic Markov process, the extended infinitesimal generator is derived, exponential martingale for the risk process is studied. The exponential bound of ruin probability in iafinite time horizon is obtained.     

On the Expected Present Value of Total Dividends in a Risk Model with Potentially Delayed Claims

In this paper, we consider a risk model in which two types of individual claims, main claims and by-claims, are defined. Every by-claim is induced by the main claim randomly and may be delayed for one time period with a certain probability. The dividend policy that certain amount of dividends will be paid as long as the surplus is greater than a constant dividend barrier is also introduced into this delayed claims risk model. By means of the probability generating functions, formulae for the expected present value of total dividend payments prior to ruin are obtained for discrete-type individual claims. Explicit expressions for the corresponding results are derived for K n claim amount distributions. Numerical illustrations are also given.     

Extremes of threshold-dependent Gaussian processes

In this paper,we are concerned with the asymptotic behavior,as u→∞,of P{sup_t∈|0,T|X_u(t)u},where X_u(t),t∈|0,T|,u0 is a family of centered Gaussian processes with continuous trajectories.A key application of our findings concerns P{sup_t∈|0,T|(X(t)+g(t))u},as u→∞,for X a centered Gaussian process and g some measurable trend function.Further applications include the approximation of both the ruin time and the ruin probability of the Brownian motion risk model with constant force of interest.     

The ruin probability of the renewal model with constant interest force and upper-tailed independent heavy-tailed claims

In this paper, we obtain the uniform estimate for discounted aggregate claims in the continuous-time renewal model of upper-tailed independent and heavy-tailed random variables. With constant interest force and constant premium rate, we establish a uniform simple asymptotic formula for ruin probability of the renewal model in the case where the initial surplus is large.     

具有Vasicek利率的风险过程的破产概率的分解(英文)

In this paper, it is assumed that an insurer with a jump-diffusion risk process would invest its surplus in a bond market, and the interest structure of the bond market is assumed to follow the Vasicek interest model. This paper focuses on the studying of the ruin problems in the above compounded process. In this compounded risk model, ruin may be caused by a claim or oscillation. We decompose the ruin probability for the compounded risk process into two probabilities： the probability that ruin caused by a claim and the probability that ruin caused by oscillation. Integro-differential equations for these ruin probabilities are derived. When the claim sizes are exponentially distributed, the above-mentioned integro-differential equations can be reduced into a three-order partial differential equation.     

MULTI-DIMENSIONAL MARKOV CHAIN–BASED ANALYSIS OF CONFLICT PROBABILITY FOR SPECTRUM RESOURCE SHARING

In this paper, we consider the optimal problem of channels sharing with heterogeneous traffic(real-time service and non-real-time service) to reduce the data conflict probability of users. Moreover, a multi-dimensional Markov chain model is developed to analyze the performance of the proposed scheme. Meanwhile, performance metrics are derived. Numerical results show that the proposed scheme can effectively reduce the forced termination probability, blocking probability and spectrum utilization.     

LAPLACE TRANSFORM OF THE SURVIVAL PROBABILITY UNDER SPARRE ANDERSEN MODEL

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.     

Survival probability and ruin probability of a risk model

In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special casc cxponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.     

Pointwise lower and upper bounds for eigenfunctions of ordinary differential operators

Summary For a differential operatorL as defined in (2.1) we consider the eigenvalue problemL u=u and describe a method to obtain a pointwise bound |u–v| wherev denotes the Rayleigh-Ritz approximation to an exact eigenfunctionu. The upper bound is continuous, but only piecewise differentiable and calculated by solving certain (inverse-positive!) auxiliary problems.Our method uses well-known estimations for (t _i) at a finite number of pointst _i[a, b] to calculate an upper, bound in the whole interval [a, b].The author would like to, thank the Battelle Institute Geneve for their assistance     

On Large Oscillations of the Remainder of the Prime Number Theorems

Under the assumption of the appropriate Ricmann hypothesis it is shown that max _tx min _l1 t ^-1/2 ((x, q, 1) – (x, q, l)) > ( – ) log₃ x and min _tx max _l1 t ^-1/2 ((x, q, 1) – (x, q, l)) < –( – ) log₃ x for x > x ₀(q, ). The proof is quite elementary, and x ₀ can be estimated effectively. As a by-product a formula for the k-th power moment of certain normed error terms is obtained.     

Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials

We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities on the classes of periodic infinitely differentiable functions C C whose elements can be represented in the form of convolutions with fixed generating kernels. We obtain asymptotic equalities for upper bounds of approximations by interpolation trigonometric polynomials on the classes C _, and C H .Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 4, pp. 495–505, April, 2004.     

Trigonometric Widths of the Classes L β,p Ψ of Functions of Many Variables

We obtain order estimates for the trigonometric widths of the classes L _,p of periodic functions of many variables in the space L _q for 1 < p 2 q < p/(p – 1).     

Zur Spektralinvarianz von Algebren von Pseudodifferentialoperatoren in derL p -Theorie

Zusammenfassung Die Hörmander-Klassen _1, ⁰ (0<1) von Pseudodifferentialoperatoren sind -Algebren. Insbesondere ist die Inverse eines inL(L ^p ( ⁿ )) invertierbaren Pseudodifferentialoperators der Klasse _1, ⁰ selbst wieder ein Pseudodifferential-operator derselben Klasse.Der Beweis beruht auf den von R. Beals, R. R. Coifman, Y. Meyer und H. O. Cordes entwickelten Methoden zur Charakterisierung von Algebren von Pseudodifferentialoperatoren.     

G-convergence of periodic parabolic operators with a small parameter by the time derivative

In this paper, we consider a sequenceP ^k of divergent parabolic operators of the second order, which are periodic in time with periodT=const, and a sequenceP ^k of shifts of these operators by an arbitrary periodic vector function X=L²((0,T) × )ⁿ where is a bounded Lipschitz domain in the space ⁿ. The compactness of the family {P ^k ¦ X, k ink with respect to strongG-convergence, the convergence of arbitrary solutions of the equations with the operatorP ^k , and the local character of the strongG-convergence in are proved under the assumptions that the matrix of coefficients ofL ² is uniformly elliptic and bounded and that their time derivatives are uniformly bounded in the space L²(;L²(0,T)).Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 4, pp. 525–538, April, 1993.     

On the Central Limit Theorem for Non-Archimedean Diophantine Approximations

We consider a Diophantine inequality:on the set of formal Laurent series of negative degree. We show that under these two conditions: (i) qⁿ(n) is a monotone non-increasing and (ii) _nqⁿ(n)=, a central limit theorem holds for the number of solutions. The proof is based on the construction of a non-stationary one dependent process associated with the Diophantine inequality.Mathematics Subject Classification (2000): 11J61, 11K60     

Upper bounds of best one-sided approximations of the classes WrLΨ in the metric of L

The lowest upper bound is obtained for best one-sided approximations of classes (r=1,2 ...) by trigonometric polynomials and splines of minimum deficiency with equidistant knots, in the metric of space L, where W^rL={f:f(x+2)=f(x), f^(r–1)(x) is absolutely continuous, f ^(r)L 1} and L is an Orlicz space.Translated from Matematicheskie Zametki, Vol. 22, No. 2, pp. 257–267, August, 1977.     

Einschließungsaussagen für gewöhnliche Differentialoperatoren

Summary For differential operatorsM of second order (as defined in (1.1)) we describe a method to prove Range-Domain implications—Mu–u and an algorithm to construct these functions , , , . This method has been especially developed for application to non-inverse-positive differential operators. For example, for non-negativea ₂ and for given functions = we require =C ₀[0, 1] C ₂([0, 1]–T) whereT is some finite set), (M) (t)(t), (t[0, 1]–T) and certain additional conditions for eachtT. Such Range-Domain implications can be used to obtain a numerical error estimation for the solution of a boundary value problemMu=r; further, we use them to guarantee the existence of a solution of nonlinear boundary value problems between the bounds- and .     

The Hilbert–Poincaré Series for Some Algebras of Invariants of Cyclic Groups

Let be a linear representation of a finite group over a field of characteristic 0. Further, let R be the corresponding algebra of invariants, and let P (t) be its Hilbert–Poincaré series. Then the series P (t) represents a rational function (t)/(t). If R is a complete intersection, then (t) is a product of cyclotomic polynomials. Here we prove the inverse statement for the case where is an almost regular (in particular, regular) representation of a cyclic group. This yields an answer to a question of R. Stanley in this very special case. Bibliography: 3 titles.