Dynamic Proportional Reinsurance and Approximations for Ruin Probabilities in the Two-Dimensional Compound Poisson Risk Model
We consider the dynamic proportional reinsurance in a two-dimensional compound Poisson risk model. The optimization in the sense of minimizing the ruin probability which is defined by the sum of subportfolio is being ruined. Via the Hamilton-Jacobi-Bellman approach we find a candidate for the optima...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/802518 |
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| author | Yan Li Guoxin Liu |
| author_facet | Yan Li Guoxin Liu |
| author_sort | Yan Li |
| collection | DOAJ |
| description | We consider the dynamic proportional reinsurance in a two-dimensional compound Poisson risk model. The optimization in the sense of minimizing the ruin probability which is defined by the sum of subportfolio is being ruined. Via the Hamilton-Jacobi-Bellman approach we find a candidate for the optimal value function and prove the verification theorem. In addition, we obtain the Lundberg bounds and the Cramér-Lundberg approximation for the ruin probability and show that as the capital tends to infinity, the optimal strategies converge to the asymptotically optimal constant strategies. The asymptotic value can be found by maximizing the adjustment coefficient. |
| format | Article |
| id | doaj-art-7f8a63da992f45cd9df860d7e4c7eac3 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-7f8a63da992f45cd9df860d7e4c7eac32025-02-03T06:12:46ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/802518802518Dynamic Proportional Reinsurance and Approximations for Ruin Probabilities in the Two-Dimensional Compound Poisson Risk ModelYan Li0Guoxin Liu1School of Insurance and Economics, University of International Business and Economics, Beijing 100029, ChinaSchool of Science, Hebei University of Technology, Tianjin 300130, ChinaWe consider the dynamic proportional reinsurance in a two-dimensional compound Poisson risk model. The optimization in the sense of minimizing the ruin probability which is defined by the sum of subportfolio is being ruined. Via the Hamilton-Jacobi-Bellman approach we find a candidate for the optimal value function and prove the verification theorem. In addition, we obtain the Lundberg bounds and the Cramér-Lundberg approximation for the ruin probability and show that as the capital tends to infinity, the optimal strategies converge to the asymptotically optimal constant strategies. The asymptotic value can be found by maximizing the adjustment coefficient.http://dx.doi.org/10.1155/2012/802518 |
| spellingShingle | Yan Li Guoxin Liu Dynamic Proportional Reinsurance and Approximations for Ruin Probabilities in the Two-Dimensional Compound Poisson Risk Model Discrete Dynamics in Nature and Society |
| title | Dynamic Proportional Reinsurance and Approximations for Ruin Probabilities in the Two-Dimensional Compound Poisson Risk Model |
| title_full | Dynamic Proportional Reinsurance and Approximations for Ruin Probabilities in the Two-Dimensional Compound Poisson Risk Model |
| title_fullStr | Dynamic Proportional Reinsurance and Approximations for Ruin Probabilities in the Two-Dimensional Compound Poisson Risk Model |
| title_full_unstemmed | Dynamic Proportional Reinsurance and Approximations for Ruin Probabilities in the Two-Dimensional Compound Poisson Risk Model |
| title_short | Dynamic Proportional Reinsurance and Approximations for Ruin Probabilities in the Two-Dimensional Compound Poisson Risk Model |
| title_sort | dynamic proportional reinsurance and approximations for ruin probabilities in the two dimensional compound poisson risk model |
| url | http://dx.doi.org/10.1155/2012/802518 |
| work_keys_str_mv | AT yanli dynamicproportionalreinsuranceandapproximationsforruinprobabilitiesinthetwodimensionalcompoundpoissonriskmodel AT guoxinliu dynamicproportionalreinsuranceandapproximationsforruinprobabilitiesinthetwodimensionalcompoundpoissonriskmodel |