This chapter first present a solution (in terms of Laplace transforms) for a history-independent shock model when the underlying shock process is a renewal process. Then the chapter states a fairly general result for history dependent shock models with arbitrary underlying shock processes. It applies this result to the specific settings with renewal shock process. The chapter discusses the generalization of the classical extreme shock model to the history-dependent case when the external shocks arrive according to a renewal process. It discusses an important proposition which provides a new perspective on the generalized extreme shock models.

Controlled Vocabulary Terms

Laplace transforms