On a gamma series expansion for the time-dependent probability of collective ruin

In the framework of the extended classical risk model with constant force of real interest i, we investigate when it is suitable to represent the probability of collective survival U(x,t) of an insurance company with initial capital x and time horizon t as a gamma series. Moreover, we derive exact analytical solutions for exponentially distributed claim sizes and integer values of λ/i, where λ is the risk parameter. As a by-product we observe that numerical procedures for estimating U(x,t) are very accurate.