英文标题：
《An optimization approach to adaptive multi-dimensional capital
management》
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作者：
G.A. Delsing, M.R.H. Mandjes, P.J.C. Spreij, E.M.M. Winands
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最新提交年份：
2018
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英文摘要：
Firms should keep capital to offer sufficient protection against the risks they are facing. In the insurance context methods have been developed to determine the minimum capital level required, but less so in the context of firms with multiple business lines including allocation. The individual capital reserve of each line can be represented by means of classical models, such as the conventional Cram\\\'{e}r-Lundberg model, but the challenge lies in soundly modelling the correlations between the business lines. We propose a simple yet versatile approach that allows for dependence by introducing a common environmental factor. We present a novel Bayesian approach to calibrate the latent environmental state distribution based on observations concerning the claim processes. The calibration approach is adjusted for an environmental factor that changes over time. The convergence of the calibration procedure towards the true environmental state is deduced. We then point out how to determine the optimal initial capital of the different business lines under specific constraints on the ruin probability of subsets of business lines. Upon combining the above findings, we have developed an easy-to-implement approach to capital risk management in a multi-dimensional insurance risk model.
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中文摘要：
企业应保留资本，以充分防范其面临的风险。在保险领域，已开发出确定所需最低资本水平的方法，但在具有多个业务线（包括分配）的公司中，这种方法较少。各条线的个人资本储备可以用经典模型表示，如传统的Cram{e}r-Lundberg模型，但挑战在于对业务线之间的相关性进行合理建模。我们提出了一种简单而通用的方法，通过引入一个共同的环境因素来实现依赖性。我们提出了一种新的贝叶斯方法来校准潜在的环境状态分布的基础上观察索赔过程。校准方法根据随时间变化的环境因素进行调整。推导了校准过程向真实环境状态的收敛性。然后，我们指出了在特定的破产概率约束下，如何确定不同业务线的最优初始资本。结合上述发现，我们在多维保险风险模型中开发了一种易于实施的资本风险管理方法。
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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：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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