Ruin Probabilities for a Risk Model with Two Classes of Claims
In this paper we consider a risk model with two kinds of claims, whose claims number processes are Poisson process and ordinary renewal process respectively. For this model, the surplus process is not Markovian, however, it can be Markovianized by introducing a supplementary process, We prove the Ma...
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| Veröffentlicht in: | Acta mathematica Sinica. English series 2010-09, Vol.26 (9), p.1749-1760 |
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| container_title | Acta mathematica Sinica. English series |
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| creator | Lv, Tong Ling Guo, Jun Yi Zhang, Xin |
| description | In this paper we consider a risk model with two kinds of claims, whose claims number processes are Poisson process and ordinary renewal process respectively. For this model, the surplus process is not Markovian, however, it can be Markovianized by introducing a supplementary process, We prove the Markov property of the related vector processes. Because such obtained processes belong to the class of the so-called piecewise-deterministic Markov process, the extended infinitesimal generator is derived, exponential martingale for the risk process is studied. The exponential bound of ruin probability in iafinite time horizon is obtained. |
| doi_str_mv | 10.1007/s10114-010-8091-x |
| format | Article |
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The exponential bound of ruin probability in iafinite time horizon is obtained.</description><subject>Generators</subject><subject>Horizon</subject><subject>Markov analysis</subject><subject>Markov processes</subject><subject>Martingales</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Poisson过程</subject><subject>Probability</subject><subject>Random variables</subject><subject>Risk</subject><subject>Studies</subject><subject>Vectors (mathematics)</subject><subject>向量马尔可夫过程</subject><subject>更新过程</subject><subject>破产概率</subject><subject>索赔次数</subject><subject>风险模型</subject><subject>风险过程</subject><issn>1439-8516</issn><issn>1439-7617</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>BENPR</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp9kEtLAzEUhQdRsFZ_gLvBjavR3Ekmj40gxRdUlFLXIZPJtGmnkzbp0PrvTZmC4MK7uWfxncPhJMk1oDtAiN0HQAAkQ4AyjgRk-5NkAASLjFFgp0fNC6DnyUUIC4SKQiA6SB4mnW3TT-9KVdrGbq0Jae18qtKJDcv03VWmSXd2O0-nO5eOGhVCJFx9kHYVLpOzWjXBXB3_MPl6fpqOXrPxx8vb6HGcaczINisoYIIUY5prIXIwICqdK85VhQtlmDG1oLnhghY5UaDKPOelKMtKa2pqXOFhctvnrr3bdCZs5coGbZpGtcZ1QXLgHBMCIpI3f8iF63wby0lGKKbxighBD2nvQvCmlmtvV8p_S0DysKfs95RxT3nYU-6jJ-89IbLtzPjf4P9MxzZ67trZJvpkqfSyto2RuAAMhCH8A_4EgoU</recordid><startdate>20100901</startdate><enddate>20100901</enddate><creator>Lv, Tong Ling</creator><creator>Guo, Jun Yi</creator><creator>Zhang, Xin</creator><general>Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society</general><general>Springer Nature B.V</general><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>~WA</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KR7</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20100901</creationdate><title>Ruin Probabilities for a Risk Model with Two Classes of Claims</title><author>Lv, Tong Ling ; 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| subjects | Generators Horizon Markov analysis Markov processes Martingales Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Poisson过程 Probability Random variables Risk Studies Vectors (mathematics) 向量马尔可夫过程 更新过程 破产概率 索赔次数 风险模型 风险过程 |
| title | Ruin Probabilities for a Risk Model with Two Classes of Claims |
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