an:05961810
Zbl 1237.91124
Cheung, Eric C. K.; Landriault, David; Badescu, Andrei L.
On a generalization of the risk model with Markovian claim arrivals
EN
Stoch. Models 27, No. 3, 407-430 (2011).
00285838
2011
j
91B30 60K15 60J75
combination of exponentials; discounted density; Gerber-Shiu function; Markovian arrival process
Summary: The class of risk models with Markovian arrival process (MAP, see e.g., [\textit{M. F. Neuts}, J. Appl. Probab. 16, 764--774 (1979; Zbl 0422.60043)]) is generalized by allowing the waiting times between two successive events (which can be a change in the environmental state and/or a claim arrival) to have an arbitrary distribution. Using a probabilistic approach, we determine the solution for a class of Gerber-Shiu functions apart from some unknown constants when claim sizes have a mixed exponential distribution. Such constants are later determined using the more classic ruin-analytic approach. A numerical example is later considered to illustrate the tractability of the suggested methodology in the study of Gerber-Shiu functions.
Zbl 0422.60043