Applied stochastic models in business and industry vol:19 issue:2 pages:147-167
We present a general risk model where the aggregate claims, as well as the premium function, evolve by jumps. This is achieved by incorporating a Levy process into the model. This seeks to account for the discrete nature of claims and asset prices. We give several explicit examples of Levy processes that can be used to drive a risk model. This allows us to incorporate aggregate claims and premium fluctuations in the same process. We discuss important features of such processes and their relevance to risk modeling. We also extend classical results on ruin probabilities to this model. Copyright (C) 2003 John Wiley Sons, Ltd.