Asymptotic analysis of ruin probabilities for bidimensionalrenewal risk models with stochastic interest return

破产概率是精算数学和概率统计学重要的研究对象之一，也是风险论的核心。 关于破产论的研究最早可以追溯到20世纪初，到目前为止，破产概率的主要研 究方法有两种，分别为更新论证方法和鞅方法。本文主要在随机投资收益下对二 维风险模型的破产概率做渐近分析，首先，我们对所用的风险模型做了如下假设， 保险公司经营两类险种，两类索赔额是相互独立的随机变量并且都属于正则变化 分布族，索赔时间同时到达；同时，保险公司可以投资于无风险资产和风险资产， 投资组合的价格过程假定为几何lévy过程{eRt，t≥0}(亦即收益率也是一个随机 过程)，在这些假设下，我们将现有的一维随机投资收益下保险...Ruin probability is one of the important subjects of actuarial mathematics and probability statistics, and also the core of risk theory. The bankruptcy theory can be traced back to the early 20th century, so far, there are two main research methods of ruin probabilities, renewal demonstration method and martingale method. In this paper, we focus on asymptotic analysis of the ruin probabilities...学位：经济学硕士院系专业：经济学院_统计学学号：1542014115199

Asymptotics for ultimate ruin probability in a by-claim risk model

This paper considers a by-claim risk model with constant interest rate in which the main claim and by-claim random vectors form a sequence of independent and identically distributed random pairs with each pair obeying some certain dependence or arbitrary dependence structure. Under the assumption of heavy-tailed claims, we derive some asymptotic formulas for ultimate ruin probability. Some simulation studies are also performed to check the accuracy of the obtained theoretical results via the crude Monte Carlo method

Uniform asymptotics for the tail probability of weighted sums with heavy tails

This paper studies the tail probability of weighted sums of the form $\sum_{i=1}^n c_i X_i$, where random variables $X_i$'s are either independent or pairwise quasi-asymptotical independent with heavy tails. Using $h$-insensitive function, the uniform asymptotic equivalence of the tail probabilities of $\sum_{i=1}^n c_iX_i$, $\max_{1\le k\le n}\sum_{i=1}^k c_iX_i$ and $\sum_{i=1}^n c_iX_i^+$ is established, where $X_i$'s are independent and follow the long-tailed distribution, and $c_i$'s take value in a broad interval. Some further uniform asymptotic results for the weighted sums of $X_i$'s with dominated varying tails are obtained. An application to the ruin probability in a discrete-time insurance risk model is presented

Uniform Asymptotics For the Tail Probability of Weighted Sums With Heavy Tails

This paper studies the tail probability of weighted sums of the form ∑i=1nciXi, where random variables X i\u27s are either independent or pairwise quasi-asymptotically independent with heavy tails. Using the idea of uniform long-tailedness, the uniform asymptotic equivalence of the tail probabilities of ∑i=1nciXi, max1≤k≤n∑i=1kciXi and ∑i=1nciXi+ is established, where X i\u27s are independent and follow the long-tailed distribution, and c i\u27s take value in a broad interval. Some further uniform asymptotic results for the weighted sums of X i\u27s with dominated varying tails are obtained. An application to the ruin probability in a discrete-time insurance risk model is presented. © 2014 Elsevier B.V

Asymptotic Finite-Time Ruin Probabilities for a Class of Path-Dependent Heavy-Tailed Claim Amounts Using Poisson Spacings

In the compound Poisson risk model, several strong hypotheses may be found too restrictive to describe accurately the evolution of the reserves of an insurance company. This is especially true for a company that faces natural disaster risks like earthquake or flooding. For such risks, claim amounts are often inter-dependent and they may also depend on the history of the natural phenomenon. The present paper is concerned with a situation of this kind where each claim amount depends on the previous interclaim arrival time, or on past interclaim arrival times in a more complex way. Our main purpose is to evaluate, for large initial reserves, the asymptotic finite-time ruin probabilities of the company when the claim sizes have a heavy-tailed distribution. The approach is based more particularly on the analysis of spacings in a conditioned Poisson process.Risk process; finite-time ruin probabilities; asymptotic approximation for large initial reserves; path-dependent claims, heavy-tailed claim amounts; Poisson spacing;

Cox risk model with variable premium rate and stochastic return on investment

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