Cramér-Lundberg approximations for ruin probabilities of risk processes perturbed by diffusion

In the present paper risk processes perturbed by diffusion are considered. By exponential tilting the processes are inbedded in an exponential family of stochastic processes, such that the type of process is preserved. By change of measure techniques asymptotic expressions for the ruin probability are obtained. This proves that the coefficients obtained by Furrer and Schmidli (1994) are the adjustment coefficients.