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摘要翻译：
菲利斯等人。（2008）提出了一个模型，用于在给定时间段结束时一组公司之间的违约模式。模型中的成分是一个图，其中顶点对应于企业，边描述企业之间的相互依赖网络，每个顶点的一个参数捕捉该企业的个别违约倾向，每个边的一个参数捕捉两个相连企业的共同违约倾向。通过识别违约模型中的违约公司集和伊辛模型中自旋为+1的站点集，相关违约模型可以在图上被重新改写为标准伊辛模型。我们问是否有一个合适的连续时间马尔可夫链取值于顶点集的子集，使得链的初始状态为空集，链的每一跳都包含一个额外的顶点，链在某个固定时域时间的分布是缺省模型给出的，而链在其他时间的分布是用与缺省模型相同族中的概率分布来描述的。我们对三个简单但在财务上自然的特殊情况表明，这是不可能的，除非是在公司之间完全独立的琐碎情况下。
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英文标题：
《Non-existence of Markovian time dynamics for graphical models of
correlated default》
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作者：
Steven N. Evans and Alexandru Hening
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最新提交年份：
2010
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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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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一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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英文摘要：
Filiz et al. (2008) proposed a model for the pattern of defaults seen among a group of firms at the end of a given time period. The ingredients in the model are a graph, where the vertices correspond to the firms and the edges describe the network of interdependencies between the firms, a parameter for each vertex that captures the individual propensity of that firm to default, and a parameter for each edge that captures the joint propensity of the two connected firms to default. The correlated default model can be re-rewritten as a standard Ising model on the graph by identifying the set of defaulting firms in the default model with the set of sites in the Ising model for which the spin is +1. We ask whether there is a suitable continuous time Markov chain taking values in the subsets of the vertex set such that the initial state of the chain is the empty set, each jump of the chain involves the inclusion of a single extra vertex, the distribution of the chain at some fixed time horizon time is the one given by the default model, and the distribution of the chain for other times is described by a probability distribution in the same family as the default model. We show for three simple but financially natural special cases that this is not possible outside of the trivial case where there is complete independence between the firms.
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PDF链接：
https://arxiv.org/pdf/1008.2226
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