Uniform asymptotics for ruin probability of a two-dimensional dependent renewal risk model

ABSTRACT

In this paper we consider the tail behavior of a two-dimensional dependent renewal risk model with two dependent classes of insurance business, in which the claim sizes are governed by a common renewal counting process, and their inter-arrival times are dependent, identically distributed. For the case that the claim size distribution belongs to the intersection of long-tailed distribution class and dominant variation class, we obtain an asymptotic formula, which holds uniformly for all time in an infinite interval. Moreover, we point out that the formula still holds uniformly for all time in an infinite interval for widely dependent random variables (r.v.s) under some conditions.     

河南学人与甲骨学研究

殷墟甲骨文被发现后 ,1 0 0年来已发展为一门国际“显学”。河南学人在甲骨文的发掘、整理、刊布、研究等方面都卓有成效 ,是甲骨学和殷商文化研究界的一支重要的学术力量。     

殷墟墓葬中青铜生产工具组合的初步研究

自1928年殷墟开始科学考古以来,殷墟墓葬中出土了大量的青铜工具,这些青铜工具种类丰富,数量较多,是当时中国能够制造的最先进的工具。本文重点考察殷墟墓葬中出土的青铜工具的种类、数量及组合方面所具有的特点,揭示殷墟青铜工具组合是以木工工具为主的组合,并着重论述青铜工具在殷墟墓葬器物组合中所具有的特殊意义。     

Dependent Insurance Risk Model: Deterministic Threshold

This article considers a dependent insurance risk model. We assume that the inter-arrival time depends on the previous claim size through a deterministic threshold structure. Adjustment coefficient and Lundberg-type upper bound for the ruin probability are obtained. In case of exponential claim size, an explicit solution for the ruin probability is obtained by solving a system of ordinary delay differential equations. Some numerical results are included for illustration purposes.     

The Ruin Probability of a Discrete-Time Risk Model with a One-Sided Linear Claim Process

In this article, the ruin probability is examined in a discrete time risk model with a constant interest rate, in which the dependent claims are assumed to have a one-sided linear structure. An explicit asymptotic formula is obtained for the ruin probability. Generalized Lundberg inequalities for the ruin probability are derived by martingale and inductive approaches.     

Second order tail behaviour of randomly weighted heavy-tailed sums and their maxima

Abstract

In this paper the second order asymptotics of the tail probabilities of randomly weighted sums and their maxima are established in the case that the underlying primary random variables are subexponential. No any assumption is made on the dependence structure between the random weights, but we assume these weights are bounded away from zero and infinity.     

On occupation times for a risk process with reserve-dependent premium

Consider a risk reserve process under which the reserve can generate interest. For constants a and b such that a<b, we study the occupation time T _a,b (t), which is the total length of the time intervals up to time t during which the reserve is between a and b. We first present a general formula for piecewise deterministic Markov processes, which will be used for the computation of the Laplace transform of T _a,b (t). Explicit results are then given for the special case that claim sizes are exponentially distributed. The classical model is discussed in detail.     

从殷墟墓葬看商代社会等级分化

从殷墟发掘墓葬的形制规模及随葬品可以看出,商代晚期社会等级分化相当明显,也相当普遍.不同家族有等级分化,同一家族内部也有等级分化.殷墟王陵明显分为东西两区,或许就是王室分化在埋葬制度上的反映.     

Gambler’s Ruin: The Duration of Play

We study the gambler’s ruin problem with a general distribution of the payoffs in each game. Assuming the expected value of the payoff distribution is negative, so that eventual ruin occurs with probability 1, we are interested in the distribution of the duration to ruin, also known as the first-passage time distribution. A generating function for this distribution is obtained. Exact expressions for the expected value and variance of this distribution, as well as asymptotic expressions for the case of large initial wealth, are derived.     

Ruin Probabilities for the Perturbed Compound Poisson Risk Process with Investment

In this article, we consider the perturbed compound Poisson risk process with investment incomes. The risk reserve process is perturbed by an independent Brownian motion and the surplus is invested at a constant force of interest. We investigate the asymptotic behavior of the ruin probability as the initial reserve goes to infinity. Bounds and time-dependent bounds are derived for the ultimate ruin probability and the probabilities of ruin within finite time, respectively. We also obtain an explicit expression for the Laplace transform of the ultimate ruin probability.