Joint distributions of some actuarial random vectors containing the time of ruin

In this paper, we introduce the renewal measure of the defective renewal sequence constituted by the zero points of the classical risk model U(t),t≥0. The density function of this renewal measure is derived. By this density function together with the strong Markov property of the surplus process, we obtain the explicit expressions for the ruin probability and the joint distributions of actuarial random vectors (T,U(T−),|U(T)|) and (T,U(T−),|U(T)|,sup0≤t<T U(t),supT≤t<L U(t),inf0≤t<L U(t)), where T represents the time of ruin and L the time of the surplus process leaving zero ultimately. Finally, a special case with the claim amount being exponentially distributed is considered.