英文标题：
《Computation of ruin probabilities for general discrete-time Markov
  models》
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作者：
Ilya Tkachev and Alessandro Abate
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最新提交年份：
2013
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英文摘要：
  We study the ruin problem over a risk process described by a discrete-time Markov model. In contrast to previous studies that focused on the asymptotic behaviour of ruin probabilities for large values of the initial capital, we provide a new technique to compute the quantity of interest for any initial value, and with any given precision. Rather than focusing on a particular model for risk processes, we give a general characterization of the ruin probability by providing corresponding recursions and fixpoint equations. Since such equations for the ruin probability are ill-posed in the sense that they do not allow for unique solutions, we approximate the ruin probability by a two-barrier ruin probability, for which fixpoint equations are well-posed. We also show how good the introduced approximation is by providing an explicit bound on the error and by characterizing the cases when the error converges to zero. The presented technique and results are supported by two computational examples over models known in the literature, one of which is extremely heavy-tailed.
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中文摘要：
我们研究了一个由离散时间马尔可夫模型描述的风险过程上的破产问题。与以往的研究相比，我们提供了一种新的技术来计算任意初始值的利息量，并且具有任意给定的精度。我们不关注风险过程的特定模型，而是通过提供相应的递归和不动点方程，给出破产概率的一般特征。由于这类破产概率方程在不允许唯一解的意义上是不适定的，因此我们用一个两障碍破产概率来近似破产概率，其中不动点方程是适定的。我们还通过提供误差的显式界以及描述误差收敛到零的情况，展示了引入的近似是多么好。所提出的技术和结果得到了文献中已知模型的两个计算实例的支持，其中一个是非常重尾的。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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