We analyze the properties of the resulting piecewise deterministic Markov process, especially its trapping risk, and discuss for which groups of people insurance can reduce trapping probability.
[X.sub.t] is a piecewise deterministic Markov process (Davis, 1984, 1993).
The advantage of the book is that it contains some material (such as the piecewise deterministic Markov process
) that may not be deeply explored in ordinary textbooks, and this is very helpful for researchers who share the same research interests with the editors.
Applying the piecewise deterministic Markov processes theory and using the relationship between the shot noise process and the accumulated/discounted aggregate claims process, the Laplace transform of the distribution of the accumulated aggregate claims is obtained.
The piecewise deterministic Markov processes theory developed by Davis (1984) is a powerful mathematical tool for examining nondiffusion models.
We derived the Laplace transform of the distribution of the shot noise process applying the piecewise deterministic Markov processes theory and the martingale.
Dassios, A., 1987, Insurance, Storage and Point Process: An Approach via Piecewise Deterministic Markov Processes, Ph.D.