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Article
Asymptotic and Numerical Solutions for Diffusion Models for Compounded Risk Reserves with Dividend Payments
International Journal of Mathematics and Mathematical Sciences
  • Sally S. L. Shao, Cleveland State University
  • C. L. Chang, Cleveland State University
Document Type
Article
Publication Date
1-1-2004
Abstract
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.
DOI
10.1155/S016117120430431X
Version
Publisher's PDF
Citation Information
S. Shao and C. L. Chang, “Asymptotic and numerical solutions for diffusion models for compounded risk reserves with dividend payments,” International Journal of Mathematics and Mathematical Sciences, vol. 2004, no. 14, pp. 721-739, 2004. doi:10.1155/S016117120430431X