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摘要翻译：
本文研究了大型保险公司的非线性正则-奇异随机最优控制问题。公司控制再保险费率和股息支付过程，以最大化股息支付的预期现值，直到破产。但是，如果最优股利门槛过低而不能被接受，则会使公司很快走向破产。此外，尽管风险和收益应该高度相关，但过度风险并不是获得高收益的良方，公司的管理者不得不对寻求超过或低于偏好风险水平的服务的公司施加他们所偏好的风险水平和额外费用。这些问题实际上是破产概率约束下的非线性正则-奇异随机最优问题。本文旨在解决这类最优问题，即推导出保险公司的最优留存率、股利支付水平、最优收益函数和最优控制策略。作为副产品，本文还提出了一个基于风险的资本标准，以确保资本需求能够覆盖给定的总风险，并给出了风险水平对最优留存率、股利支付水平和最优控制策略的影响。
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英文标题：
《Optimization of dividend and reinsurance strategies under ruin
probability constraint》
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作者：
Zongxia Liang, Jicheng Yao
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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：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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英文摘要：
This paper considers nonlinear regular-singular stochastic optimal control of large insurance company. The company controls the reinsurance rate and dividend payout process to maximize the expected present value of the dividend pay-outs until the time of bankruptcy. However, if the optimal dividend barrier is too low to be acceptable, it will make the company result in bankruptcy soon. Moreover, although risk and return should be highly correlated, over-risking is not a good recipe for high return, the supervisors of the company have to impose their preferred risk level and additional charge on firm seeking services beyond or lower than the preferred risk level. These indeed are nonlinear regular-singular stochastic optimal problems under ruin probability constraints. This paper aims at solving this kind of the optimal problems, that is, deriving the optimal retention ratio,dividend payout level, optimal return function and optimal control strategy of the insurance company. As a by-product, the paper also sets a risk-based capital standard to ensure the capital requirement of can cover the total given risk, and the effect of the risk level on optimal retention ratio, dividend payout level and optimal control strategy are also presented.
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PDF链接：
https://arxiv.org/pdf/1005.1361
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