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摘要翻译：
本文发展了一种符号方法，得到了当保费收入依赖于保险组合的现有盈余时，续保风险模型中破产概率和折现惩罚函数的渐近表达式。分析基于变系数线性常微分方程的边界问题。格林算子的代数结构允许我们发展一种处理解的渐近行为的直观方法，导致指数型展开和CRAM\'ER型渐近。此外，我们得到了复合泊松风险模型中保费函数更具体情形的闭式解。
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英文标题：
《Exact and asymptotic results for insurance risk models with
surplus-dependent premiums》
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作者：
Hansj\"org Albrecher, Corina Constantinescu, Zbigniew Palmowski, Georg
Regensburger and Markus Rosenkranz
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最新提交年份：
2011
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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：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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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 develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance portfolio. The analysis is based on boundary problems for linear ordinary differential equations with variable coefficients. The algebraic structure of the Green's operators allows us to develop an intuitive way of tackling the asymptotic behavior of the solutions, leading to exponential-type expansions and Cram\'er-type asymptotics. Furthermore, we obtain closed-form solutions for more specific cases of premium functions in the compound Poisson risk model.
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PDF链接：
https://arxiv.org/pdf/1110.5276
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