Let L be a linear space of real bounded random variables on the probability space (omega,A, P0). There is a finitely additive probability P on A, such that P tilde P0 and EP (X) = 0 for all X in L, if and only if cEQ(X) = ess sup(-X), X in L, for some constant c 0 and (countably additive)...

In this paper, we consider a risk model with two classes of insurance business studied by Yuen[3]. One claim arrival process is a Poisson, process, the other is an Erlang(2) process. With help of a good property of martingales proved in the paper, an Lundberg-like up-bound for the ultimate ruin...