On the Gerber-Shiu discounted penalty function for a surplus process described by PDMPs

Authors
He, Jing Min Wu, Rong
Citation
He, Jing Min et Wu, Rong, On the Gerber-Shiu discounted penalty function for a surplus process described by PDMPs, Acta mathematica Sinica. English series (Print) , 26(5), 2010, pp. 951-962
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
26
Issue
5
Year of publication
2010
Pages
951 - 962
Database
ACNP
SICI code
Abstract
In this paper, we investigate the Gerber-Shiu discounted penalty function for the surplus process described by a piecewise deterministic Markov process (PDMP).We derive an integral equation for the Gerber-Shiu discounted penalty function, and obtain the exact solution when the initial surplus is zero. Dickson formulae are also generalized to the present surplus process.