随机利率下的双险种风险模型

在随机利率风险模型中,将单险种推广为双险种,推导出风险调节系数和破产概率的一般表达式.     

常利率复合二项双险种风险模型的研究

提出了含利率因素的复合二项双险种风险模型,并在有关假设的基础上,给出了此模型下保险公司稳定经营的必要条件;证明了索赔时刻的盈余过程是一马氏过程和调节系数的存在性,并采用递归方法得到了模型的破产概率的上界估计.     

双险种的Cox风险模型

由于保险公司经营规模的不断扩大，险种类型的增多，用古典风险模型及其其它推广的单一险种风险模型来研究其风险经营过程存在着局限性，因而需要建立多险种的风险模型。本文研究了一类两种险种且理赔次数服从Cox过程的模型。得到了破产概率满足推广的Lundberg不等式。以及在特殊情况时ψ（0）的明确表达式。     

带利率的特殊双险种风险模型的破产概率

研究了保费为一复合随机过程且含利率因素的特殊双险种风险模型,给出了此模型下保险公司稳定经营的必要条件;证明了调节系数的存在性;用鞅方法讨论了此模型的破产概率上界.     

理赔为一般到达的常利率风险模型

本文研究了一般到达的常利率保险风险问题，应用建立Markov骨架过程的方法建立了理赔为一般到达的常利率风险模型．给出了破产时的余额分布、破产前瞬间的余额分布、破产时间与破产前瞬间余额的联合分布、破产时间与破产时余额的联合分布及破产前瞬间余额、破产时余额与破产时间的联合分布．     

一类带干扰的多险种风险模型

本文考虑一类带干扰的两独立险种的风险模型,其中两索赔次数过程分别为Poisson过程和Elang(2)过程.主要得出该模型的生存概率所满足的积分-微分方程和破产概率的渐近性.     

一类延迟双险种风险模型的破产概率

本考虑了一类索赔发生分别是Poisson过程和Erlang(n)过程的延迟双险种模型，给出了初始女本为u的破产概率ψ(u)表达式．     

一类常利率下的复合Poisson-Geometric过程风险模型

将文献[6]中常利率情况下的风险模型,推广为索赔来到过程为Poisson-Geometric过程的风险模型.给出了该模型初始资产为u时生存概率所满足的积分方程,并更正了文献[6]中的错误。     

索赔次数为复合Poisson-Geometric过程的常利率风险模型

讨论了常利率下索赔次数为复合Po issong-G eom etric过程的风险模型的破产概率,得到了破产概率所满足的积分方程.     

常利率环境下带干扰风险模型的破产估计

本文中，我们研究具有固定收益率或利率的带干扰的复合泊瓦松风险模型的破产概率，给出破产概率估计，及上下界。     

带利息力的随机双险种风险模型

由于经典风险模型及其拓展模型的局限性,因而构造了一种带利息力的随机双险种风险模型,并且获得了初始资产为u时生存概率满足的积分方程,以及初始资产为0时生存概率的表达式.     

On the renewal risk model with interest and dividend

We consider that the reserve of an insurance company follows a renewal risk process with interest and dividend. For this risk process, we derive integral equations and exact infinite series expressions for the Gerber-Shiu discounted penalty function. Then we give lower and upper bounds for the ruin probability. Finally, we present exact expressions for the ruin probability in a special case of renewal risk processes.     

Finite-time ruin probability of a nonstandard compound renewal risk model with constant force of interest

In this paper, we establish an exact asymptotic formula for the finite-time ruin probability of a nonstandard compound renewal risk model with constant force of interest in which claims arrive in groups, their sizes in one group are identically distributed but negatively dependent, and the inter-arrival times between groups are negatively dependent too.     

带利率的更新风险模型的破产概率的上界估计

本研究了在常利率条件下普通更新风险模型的破产概率问题．采用一种递推的方法给出了这种情况下破产概率的一个上界估计．     

Exponential Bounds for Ruin Probability in Two Moving Average Risk Models with Constant Interest Rate

The authors consider two discrete-time insurance risk models. Two moving average risk models are introduced to model the surplus process, and the probabilities of ruin are examined in models with a constant interest force. Exponential bounds for ruin probabilities of an infinite time horizon are derived by the martingale method.     

Asymptotic ruin probabilities in a generalized bidimensional risk model perturbed by diffusion with constant force of interest

In the paper, we study three types of finite-time ruin probabilities in a diffusion-perturbed bidimensional risk model with constant force of interest, pairwise strongly quasi-asymptotically independent claims and two general claim arrival processes, and obtain uniformly asymptotic formulas for times in a finite interval when the claims are both long-tailed and dominatedly-varying-tailed. In particular, with a certain dependence structure among the inter-arrival times, these formulas hold uniformly for all times when the claims are pairwise quasi-asymptotically independent and consistently-varying-tailed.     

Ruin probability for correlated negative risk sums model with Erlang processes

This paper studies a Sparre Andersen negative risk sums model in which the distribution of ＂interclaim＂ time is that of a sum of n independent exponential random variables. Thus, the Erlang（n） model is a special case. On this basis the correlated negative risk sums process with the common Erlang process is considered. Integro-differential equations with boundary conditions for ψ（u） are given. For some special cases a closed-form expression for ψ（u） is derived.     

Ruin probabilities of a bidimensional risk model with investment

We consider a classical risk model with the possibility of investment. We study two types of ruin in the bidimensional framework. Using the martingale technique, we obtain an upper bound for the infinite-time ruin probability with respect to the ruin time T_max(u₁,u₂). For each type of ruin, we derive an integral-differential equation for the survival probability, and an explicit asymptotic expression for the finite-time ruin probability.     

Ruin problems for an autoregressive risk model with dependent rates of interest

In this paper, we consider a discrete insurance risk model in which the claims, the premiums and the rates of interest are assumed to have dependent autoregressive structures (AR(1)). We derive recursive and integral equations for expected discounted penalty function. By these equations, we obtain generalized Lundberg inequality for the infinite time severity of ruin and hence for the infinite time ruin probability, consider asymptotic formula for the finite time ruin probability when loss distributions have regularly varying tails, and study some probability properties of the duration of ruin.     

On the absolute ruin problem in a Sparre Andersen risk model with constant interest

In this paper, we extend the work of Mitric and Sendova (2010), which considered the absolute ruin problem in a risk model with debit and credit interest, to renewal and non-renewal structures. Our first results apply to MAP processes, which we later restrict to the Sparre Andersen renewal risk model with interclaim times that are generalized Erlang (n) distributed and claim amounts following a Matrix-Exponential (ME) distribution (see for e.g. Asmussen and O’Cinneide (1997)). Under this scenario, we present a general methodology to analyze the Gerber-Shiu discounted penalty function defined at absolute ruin, as a solution of high-order linear differential equations with non-constant coefficients. Closed-form solutions for some absolute ruin related quantities in the generalized Erlang (2) case complement the results obtained under the classical risk model by Mitric and Sendova (2010).