Asymptotic and numerical solutions for diffusion models for compounded risk reserves with dividend payments
We study a family of diffusion models for compounded risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. We are interested in the models in which the dividend payments are paid from the risk reserves. After defining the process of conditio...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120430431X |
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| author | S. Shao C. L. Chang |
| author_facet | S. Shao C. L. Chang |
| author_sort | S. Shao |
| collection | DOAJ |
| description | We study a family of diffusion models for compounded risk
reserves which account for the investment income earned and for
the inflation experienced on claim amounts. We are interested in
the models in which the dividend payments are paid from the risk
reserves. After defining the process of conditional probability
in finite time, martingale theory turns the nonlinear stochastic
differential equation to a special class of boundary value
problems defined by a parabolic equation with a nonsmooth
coefficient of the convection term. Based on the behavior of the
total income flow, asymptotic and numerical methods are used to
solve the special class of diffusion equations which
govern the conditional ruin probability over finite time. |
| format | Article |
| id | doaj-art-e2ce17267be6411b961d61072b743f07 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e2ce17267be6411b961d61072b743f072025-02-03T01:22:20ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-0120041472173910.1155/S016117120430431XAsymptotic and numerical solutions for diffusion models for compounded risk reserves with dividend paymentsS. Shao0C. L. Chang1Department of Mathematics, Cleveland State University, Cleveland 44115, OH, USADepartment of Mathematics, Cleveland State University, Cleveland 44115, OH, USAWe study a family of diffusion models for compounded risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. We are interested in the models in which the dividend payments are paid from the risk reserves. After defining the process of conditional probability in finite time, martingale theory turns the nonlinear stochastic differential equation to a special class of boundary value problems defined by a parabolic equation with a nonsmooth coefficient of the convection term. Based on the behavior of the total income flow, asymptotic and numerical methods are used to solve the special class of diffusion equations which govern the conditional ruin probability over finite time.http://dx.doi.org/10.1155/S016117120430431X |
| spellingShingle | S. Shao C. L. Chang Asymptotic and numerical solutions for diffusion models for compounded risk reserves with dividend payments International Journal of Mathematics and Mathematical Sciences |
| title | Asymptotic and numerical solutions for diffusion models for compounded risk reserves with dividend payments |
| title_full | Asymptotic and numerical solutions for diffusion models for compounded risk reserves with dividend payments |
| title_fullStr | Asymptotic and numerical solutions for diffusion models for compounded risk reserves with dividend payments |
| title_full_unstemmed | Asymptotic and numerical solutions for diffusion models for compounded risk reserves with dividend payments |
| title_short | Asymptotic and numerical solutions for diffusion models for compounded risk reserves with dividend payments |
| title_sort | asymptotic and numerical solutions for diffusion models for compounded risk reserves with dividend payments |
| url | http://dx.doi.org/10.1155/S016117120430431X |
| work_keys_str_mv | AT sshao asymptoticandnumericalsolutionsfordiffusionmodelsforcompoundedriskreserveswithdividendpayments AT clchang asymptoticandnumericalsolutionsfordiffusionmodelsforcompoundedriskreserveswithdividendpayments |