英文标题：
《Optimal excess-of-loss reinsurance for stochastic factor risk models》
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作者：
Matteo Brachetta and Claudia Ceci
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最新提交年份：
2019
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英文摘要：
We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer\'s surplus is governed by a marked point process with dual-predictable projection affected by an environmental factor and that the insurance company can borrow and invest money at a constant real-valued risk-free interest rate $r$. Our model allows for stochastic risk premia, which take into account risk fluctuations. Using stochastic control theory based on the Hamilton-Jacobi-Bellman equation, we analyze the optimal reinsurance strategy under the criterion of maximizing the expected exponential utility of the terminal wealth. A verification theorem for the value function in terms of classical solutions of a backward partial differential equation is provided. Finally, some numerical results are discussed.
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中文摘要：
研究了当理赔到达过程的强度和理赔规模分布都受到外生随机因素影响时的最优超额损失再保险问题。我们假设，保险公司的盈余由一个标记点过程控制，该过程具有受环境因素影响的双重可预测预测预测，并且保险公司可以以不变的实值无风险利率（r$）借款和投资。我们的模型考虑了考虑风险波动的随机风险溢价。利用基于Hamilton-Jacobi-Bellman方程的随机控制理论，分析了终端财富期望指数效用最大化准则下的最优再保险策略。给出了一个关于倒向偏微分方程经典解的值函数的检验定理。最后，讨论了一些数值结果。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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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：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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