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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |