A numerical method to find the probability of ultimate ruin in the classical risk model with stochastic return on investments [An article from: Insurance Mathematics and Economics]

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Description:
Let @j(y) be the probability of ultimate ruin in the classical risk process compounded by a linear Brownian motion. Here y is the initial capital. We give sufficient conditions for the survival probability function @f=1-@j to be four times continuously differentiable, which in particular implies that @f is the solution of a second order integro-differential equation. Transforming this equation into an ordinary Volterra integral equation of the second kind, we analyze properties of its numerical solution when basically the block-by-block method in conjunction with Simpsons rule is used. Finally, several numerical examples show that the method works very well.