Considering a risk model with random income,the explicit expression for the joint distribution of three variables:the time of ruin,the surplus immediately before ruin and the deficit at ruin is derived by using the technique of Wu.

Ruin probability at constant claim volume in case of ruin time;

In this paper we mainly discuss the first two moments of the ruin time T 、recovery time ~ ( = 1 , 2 , ) and the sum of recovery time ~ in the compound binomial model by renewal method and martingale method when the initial surplurs is u .

This paper studies the expected discounted penalty function associated with the time of ruin for a risk model with stochastic premium.

The classical risk process is considered and the joint distribution of the time of ruin and the loss at ruin is discussed with Lévy measure.

The explicit expression for the joint distribution of the time of ruin,the surplus immediately before ruin and the deficit at ruin is obtained according to the classical risk process with constant interest rate under a threshold dividend strategy.