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摘要翻译：
根据《巴塞尔二号准则》，操作风险（OpRisk）高级计量方法并没有就用于进行资本估计的统计模型类别作出规定。然而，使用损失分布方法(LDA)范例来建模与巴塞尔II业务线/事件类型相对应的个人OpRisk损失过程已成为公认的做法。本文导出了一类新的双随机α-稳定LDA模型族。这些模型提供了捕捉OpRisk典型的重尾损失过程的能力，同时也提供了复合过程年损失密度和分布的解析表达式，以及聚合复合过程年损失模型。特别是，我们开发了两种情况下的年度损失过程模型。第一种情形考虑了具有随机强度参数的损失过程，导致每年都有一个非齐次复合泊松过程。在这种模型下，损失的最终到达过程将在一年内对增量进行独立计数。第二种方案考虑将年损失过程离散化为每月增量，并将时间增量与二项过程相关，成功概率每年变化。这些模型中的每一个都将在LDA框架下与重尾严重性模型耦合，重尾严重性模型由每个损失事件的损失量的$\alpha$-稳定的严重性组成。本文将推导出每种模型下的年损失分布、密度和分布的解析结果，并研究它们的性质。
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英文标题：
《Analytic Loss Distributional Approach Model for Operational Risk from
the alpha-Stable Doubly Stochastic Compound Processes and Implications for
Capital Allocation》
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作者：
Gareth W. Peters, Pavel Shevchenko, Mark Young, Wendy Yip
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最新提交年份：
2011
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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：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Applications 应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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一级分类：Statistics 统计学
二级分类：Computation 计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
Under the Basel II standards, the Operational Risk (OpRisk) advanced measurement approach is not prescriptive regarding the class of statistical model utilised to undertake capital estimation. It has however become well accepted to utlise a Loss Distributional Approach (LDA) paradigm to model the individual OpRisk loss process corresponding to the Basel II Business line/event type. In this paper we derive a novel class of doubly stochastic alpha-stable family LDA models. These models provide the ability to capture the heavy tailed loss process typical of OpRisk whilst also providing analytic expressions for the compound process annual loss density and distributions as well as the aggregated compound process annual loss models. In particular we develop models of the annual loss process in two scenarios. The first scenario considers the loss process with a stochastic intensity parameter, resulting in an inhomogeneous compound Poisson processes annually. The resulting arrival process of losses under such a model will have independent counts over increments within the year. The second scenario considers discretization of the annual loss process into monthly increments with dependent time increments as captured by a Binomial process with a stochastic probability of success changing annually. Each of these models will be coupled under an LDA framework with heavy-tailed severity models comprised of $\alpha$-stable severities for the loss amounts per loss event. In this paper we will derive analytic results for the annual loss distribution density and distribution under each of these models and study their properties.
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PDF链接：
https://arxiv.org/pdf/1102.3582
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