期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2004
卷号：2004
DOI：10.1155/S016117120430431X
出版社：Hindawi Publishing Corporation
摘要：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.
