The joint distributions of some actuarial diagnostics for the jump-diffusion risk process

In this article, the joint distributions of several actuarial diagnostics which are important to insurers' running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus process leaving zero ultimately (simply, the ultimately leaving-time), the surplus immediately prior to ruin, the supreme profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. The explicit expressions for their distributions are obtained mainly by the various properties of Lévy process, such as the homogeneous strong Markov property and the spatial homogeneity property etc, moveover, the many properties for Brownian motion.