| A Large Deviation Principle for the Risk Process with Varying Premium |
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| 作者姓名： | HE Xiaoxia MING Ruixing HU Yijun |
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| 作者单位： | [1]School of Mathematics and Statistics, Wuhan University,Wuhan 430072, Hubei, China; [2]School of Mathematics and Information Sciences, JiangxiNormal University, Nanchang 330022, Jiangxi, China |
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| 基金项目： | Supported by the National Natural Science Foundation of China （70273029） |
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| 摘 要： | Let u ∈ R ,for any ω 〉 0, the processes X^ε = {X^ε（t）; 0 ≤ t≤ 1} are governed by the following random evolution equations dX^ε（t）= b（X^ε（t）,v（t））dt-εdSt/ε, where S={St; 0≤t≤1} is a compound Poisson process, the process v={v（t）; 0≤t≤1} is independent of S and takes values in R^m. We derive the large deviation principle for{（X^ε,v（.））; ε〉0} when ε↓0 by approximation method and contraction principle, which will be meaningful for us to find out the path property for the risk process of this type.
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| 关 键 词： | 风险过程 大偏差原理 溢价波动 随机进化方程 |
| 文章编号： | 1007-1202（2007）03-0412-05 |
| 收稿时间： | 28 July 2006 |
| 修稿时间： | 2006-07-28 |
A large deviation principle for the risk process with varying premium |
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| HE Xiaoxia MING Ruixing HU Yijun.A Large Deviation Principle for the Risk Process with Varying Premium[J].Wuhan University Journal of Natural Sciences,2007,12(3):412-416. |
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| Authors: | He Xiaoxia Ming Ruixing Hu Yijun |
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| Institution: | (1) School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, China;(2) School of Mathematics and Information Sciences, Jiangxi Normal University, Nanchang, 330022, Jiangxi, China |
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| Abstract: | Let u ∈ R, for any ɛ > 0, the processes X
ε = {X
ε(t); 0 ⩽ t ⩽ 1} are governed by the following random evolution equations dX
ε(t=b(X
ε(t,v(t))dt−εdS
t/ε, where S={S
t; 0 ⩽ t ⩽ 1} is a compound Poisson process, the process v={v(t); 0 ⩽ t ⩽ 1} is independent of S and takes values in R
m. We derive the large deviation principle for {(X
ε,v(·)); ge > 0} when ɛ ↓ 0 by approximation method and contraction principle, which will be meaningful for us to find out the path property for
the risk process of this type.
Biography: HE Xiaoxia (1979–), female, Ph. D. candidate, research direction: large deviations and their applications, insurance mathematics. |
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| Keywords: | large deviations varying premium compound Pois-son process |
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