Document Type

Article

Publication Date

2003

Publication Title

International Journal of Mathematics and Mathematical Sciences

Abstract

We study a family of diffusion models for risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. After we defined the process of the conditional probability of ruin over finite time and imposed the appropriate boundary conditions, classical results from the theory of diffusion processes turn the stochastic differential equation to a special class of initial and boundary value problems defined by a linear diffusion equation. Armedwith asymptotic analysis and perturbation theory, we obtain the asymptotic solutions of the diffusion models (possibly degenerate) governing the conditional probability of ruin over a finite time in terms of interest rate.

Original Citation

S. Shao, “Asymptotic solutions of diffusion models for risk reserves,” International Journal of Mathematics and Mathematical Sciences, vol. 2003, no. 35, pp. 2221-2239, 2003. doi:10.1155/S0161171203208231

DOI

10.1155/S0161171203208231

Version

Publisher's PDF

Volume

2003

Issue

35

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