摘要翻译：
本文研究了一个由带漂移的布朗运动建模的风险过程（扩散近似模型）。保险实体可以购买再保险以降低风险，并在离散时间接受现金注入以避免破产。考虑了比例再保险和超额损失再保险。目标是寻找最优的再保险和现金注入策略，使总成本最小，以保持公司剩余过程非负，即不破产，其中成本函数定义为注入的总贴现值。通过求解相应的拟变分不等式(QVIs)，显式地找到了最优解。
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英文标题：
《Minimal Cost of a Brownian Risk without Ruin》
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作者：
Shangzhen Luo and Michael Taksar
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最新提交年份：
2011
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分类信息：

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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英文摘要：
  In this paper, we study a risk process modeled by a Brownian motion with drift (the diffusion approximation model). The insurance entity can purchase reinsurance to lower its risk and receive cash injections at discrete times to avoid ruin. Proportional reinsurance and excess-of-loss reinsurance are considered. The objective is to find the optimal reinsurance and cash injection strategy that minimizes the total cost to keep the company's surplus process non-negative, i.e. without ruin, where the cost function is defined as the total discounted value of the injections. The optimal solution is found explicitly by solving the according quasi-variational inequalities (QVIs).
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PDF链接：
https://arxiv.org/pdf/1112.4005