International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 846753 | https://doi.org/10.1155/S0161171203208231

S. Shao, "Asymptotic solutions of diffusion models for risk reserves", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 846753, 19 pages, 2003. https://doi.org/10.1155/S0161171203208231

Asymptotic solutions of diffusion models for risk reserves

Received22 Aug 2002

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. Armed with 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.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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