In this paper we consider risk processes with two classes of business in which the two claim-number processes are dependent Cox processes. We first assume that the two claim-number processes have a two-dimensional Markovian intensity. Under this assumption, we not only study the sum of the two individual risk processes but also investigate the two-dimensional risk process formed by considering the two individual processes separately. For each of the two risk processes we derive an expression for the ruin probability, and then construct an upper bound for the ruin probability. We next assume that the intensity of the two claim-number processes follows a Markov chain. In this case, we examine the ruin probability of the sum of the two individual risk processes. Specifically, a differential system for the ruin probability is derived and numerical results are obtained for exponential claim sizes.
机构:
Cent South Univ, Sch Math & Stat, Changsha, Hunan, Peoples R ChinaCent South Univ, Sch Math & Stat, Changsha, Hunan, Peoples R China
Liu, Zaiming
Geng, Bingzhen
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Cent South Univ, Sch Math & Stat, Changsha, Hunan, Peoples R China
Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R ChinaCent South Univ, Sch Math & Stat, Changsha, Hunan, Peoples R China
Geng, Bingzhen
Man, Xinyue
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Cent South Univ, Sch Math & Stat, Changsha, Hunan, Peoples R ChinaCent South Univ, Sch Math & Stat, Changsha, Hunan, Peoples R China
Man, Xinyue
Liu, Xinyu
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Cent South Univ, Sch Math & Stat, Changsha, Hunan, Peoples R ChinaCent South Univ, Sch Math & Stat, Changsha, Hunan, Peoples R China
机构:
Northwestern Polytech Univ, Econ Res Ctr, Xian 710072, Peoples R ChinaNorthwestern Polytech Univ, Econ Res Ctr, Xian 710072, Peoples R China
Yang, Haizhong
Gao, Wei
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Xian Univ Finance & Econ, Sch Stat, Xian, Peoples R ChinaNorthwestern Polytech Univ, Econ Res Ctr, Xian 710072, Peoples R China
Gao, Wei
Li, Jinzhu
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Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China
Nankai Univ, LPMC, Tianjin 300071, Peoples R ChinaNorthwestern Polytech Univ, Econ Res Ctr, Xian 710072, Peoples R China
机构:
Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China
Nankai Univ, LPMC, Tianjin 300071, Peoples R ChinaNankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China
Li, Jinzhu
Yang, Haizhong
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Xian Univ Finance & Econ, Sch Stat, Xian 710100, Peoples R China
Northwestern Polytech Univ, Econ Res Ctr, Xian 710072, Peoples R ChinaNankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China