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摘要翻译：
De Finetti(1957)提出的最优股利问题最近被推广到谱负L\'evy模型，其中最优策略的实现依赖于尺度函数及其导数的计算。本文提出了最优策略的相位型拟合逼近。我们考虑了具有相位型跳跃的谱负L\'Evy过程和亚纯L\'Evy过程（Kuznetsov et al.，2010a)，并用它们的标度函数逼近一般谱负L\'Evy过程的标度函数。我们用带I.I.D的谱负L\'Evy过程的例子，解析地得到了收敛性结果，并数值地说明了逼近方法的有效性。Weibull分布跳跃、\beta族和CGMY过程。
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英文标题：
《Solving Optimal Dividend Problems via Phase-type Fitting Approximation
of Scale Functions》
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作者：
Masahiko Egami and Kazutoshi Yamazaki
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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：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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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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英文摘要：
The optimal dividend problem by De Finetti (1957) has been recently generalized to the spectrally negative L\'evy model where the implementation of optimal strategies draws upon the computation of scale functions and their derivatives. This paper proposes a phase-type fitting approximation of the optimal strategy. We consider spectrally negative L\'evy processes with phase-type jumps as well as meromorphic L\'evy processes (Kuznetsov et al., 2010a), and use their scale functions to approximate the scale function for a general spectrally negative L\'evy process. We obtain analytically the convergence results and illustrate numerically the effectiveness of the approximation methods using examples with the spectrally negative L\'evy process with i.i.d. Weibull-distributed jumps, the \beta-family and CGMY process.
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PDF链接：
https://arxiv.org/pdf/1011.4732
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