| EXPECTED DISCOUNTED PENALTY FUNCTION AT RUIN FOR RISK PROCESS PERTURBED BY DIFFUSION UNDER INTEREST FORCE |
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| 引用本文： | Zhao Xia Ouyang Zisheng. EXPECTED DISCOUNTED PENALTY FUNCTION AT RUIN FOR RISK PROCESS PERTURBED BY DIFFUSION UNDER INTEREST FORCE[J]. 高校应用数学学报(英文版), 2005, 20(3): 289-296. DOI: 10.1007/s11766-005-0004-x |
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| 作者姓名： | Zhao Xia Ouyang Zisheng |
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| 作者单位： | [1]School of Statistics, Renmin University of China, Beijing 100872 [2]Institute of Statistics and Actuary,Shandong Economic University,Jinan 250014,China. [3]Dept. of Inform. ,Hunan Business College ,Changsha 410205 ,China. |
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| 基金项目： | Supported by the National Natural Science Foundation of China（10471076） ,National Planning Project of Social Science of China （04BTJ010）, the Key Project of Chinese Ministry of Education （104053）,Shangdong Foundation of Natural Science （Y2004A05） and Shandong Planning Project of Social Science（04BJJ31 ）. |
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| 摘 要： | In this article, the risk process perturbed by diffusion under interest force is considered, the continuity and twice continuous differentiability for Фδ（u,w） are discussed,the Feller expression and the integro-differential equation satisfied by Фδ （u ,w） are derived. Finally, the decomposition of Фδ（u,w） is discussed, and some properties of each decomposed part of Фδ（u,w） are obtained. The results can be reduced to some ones in Gerber and Landry＇s,Tsai and Willmot＇s, and Wang＇s works by letting parameter δ and （or） a be zero.
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| 关 键 词： | 破产风险 处罚函数 风险过程模拟 数学分析 |
| 收稿时间： | 2005-03-09 |
Expected discounted penalty function at ruin for risk process perturbed by diffusion under interest force |
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| Zhao Xia,Ouyang Zisheng. Expected discounted penalty function at ruin for risk process perturbed by diffusion under interest force[J]. Applied Mathematics A Journal of Chinese Universities, 2005, 20(3): 289-296. DOI: 10.1007/s11766-005-0004-x |
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| Authors: | Zhao Xia Ouyang Zisheng |
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| Affiliation: | (1) School of Statistics, Renmin University of China, 100872 Beijing;(2) Institute of Statistics and Actuary, Shandong Economic University, 250014 Jinan, China;(3) Dept. of Inform., Hunan Business College, 410205 Changsha, China |
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| Abstract: | In this article, the risk process perturbed by diffusion under interest force is considered, the continuity and twice continuous differentiability for Ф δ(u,w) are discussed, the Feller expression and the integro-differential equation satisfied by Ф δ(u,w) are derived. Finally, the decomposition of Ф δ(u,w) is discussed, and some properties of each decomposed part of Ф δ(u,w) are obtained. The results can be reduced to some ones in Gerber and Landry's, Tsai and Willmot's, and Wang's works by letting parameter δ and (or) σ be zero. Supported by the National Natural Science Foundation of China (10471076), National Planning Project of Social Science of China (04BTJ010), the Key Project of Chinese Ministry of Education (104053), Shangdong Foundation of Natural Science (Y2004A05) and Shandong Planning Project of Social Science (04BJJ31). |
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| Keywords: | risk process perturbed by diffusion under interest force expected discounted penalty at ruin twice continuous differentiability integro-differential equation. |
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