Asymptotic and numerical solutions for diffusion models for risk reserves
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 which
(1) no dividend payments; and (2) the dividend payments are paid from
the risk reserves. After defined 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 non-smooth coefficient of the
convection term. Based on the behavior of the total income flow,
asymptotic and numerical methods are used to solving the special class
diffusion equations, which governing the conditional ruin probability
over finite time.
∼邵沙麗教授演講摘要∼