英文标题：
《Optimal Dividend Strategies for Two Collaborating Insurance Companies》
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作者：
Hansjoerg Albrecher and Pablo Azcue and Nora Muler
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最新提交年份：
2015
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英文摘要：
We consider a two-dimensional optimal dividend problem in the context of two insurance companies with compound Poisson surplus processes, who collaborate by paying each other\'s deficit when possible. We solve the stochastic control problem of maximizing the weighted sum of expected discounted dividend payments (among all admissible dividend strategies) until ruin of both companies, by extending results of univariate optimal control theory. In the case that the dividends paid by the two companies are equally weighted, the value function of this problem compares favorably with the one of merging the two companies completely. We identify this optimal value function as the smallest viscosity supersolution of the respective Hamilton-Jacobi-Bellman equation and provide an iterative approach to approximate it numerically. Curve strategies are identified as the natural analogue of barrier strategies in this two-dimensional context. A numerical example is given for which such a curve strategy is indeed optimal among all admissible dividend strategies, and for which this collaboration mechanism also outperforms the suitably weighted optimal dividend strategies of the two stand-alone companies.
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中文摘要：
我们考虑了一个二维最优红利问题，在两个保险公司具有复合泊松盈余过程的背景下，他们在可能的情况下通过支付彼此的赤字进行合作。通过推广单变量最优控制理论的结果，我们解决了最大化预期贴现股息支付（在所有可接受的股息策略中）的加权和直到两家公司破产的随机控制问题。在两个公司支付的股息权重相等的情况下，该问题的价值函数比完全合并两个公司的价值函数更有利。我们将此最优值函数确定为相应Hamilton-Jacobi-Bellman方程的最小粘度上解，并提供了一种迭代方法来数值逼近它。曲线策略被认为是这种二维背景下屏障策略的自然类比。文中给出了一个数值例子，说明这种曲线策略在所有可接受的股利策略中确实是最优的，并且这种协作机制也优于两个独立公司的适当加权最优股利策略。
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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：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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