| The First Two Moments of Aggregate Claims in a Markovian Environment |
| Received:March 19, 2009 Revised:September 18, 2009 |
| Key Words:
discrete-time insurance risk model discounted aggregate claims circumstance process moment.
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| Fund Project:Supported by the Funds for Frontier Interdisciplines of DUT in 2010 (Grant No.DUT10JS06). |
| Author Name | Affiliation | | Yu Jie HUANG | School of Mathematical Science, Dalian University of Technology, Liaoning 116024, P. R. China
Department of Mathematics, Anshan Normal University, Liaoning 114005, P. R. China | | Jing Hai FENG | School of Mathematical Science, Dalian University of Technology, Liaoning 116024, P. R. China
| | Li Xin SONG | School of Mathematical Science, Dalian University of Technology, Liaoning 116024, P. R. China
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| Abstract: |
| We consider the discounted aggregate claims when the insurance risks and financial risks are governed by a discrete-time Markovian environment. We assume that the claim sizes and the financial risks fluctuate over time according to the states of economy, which are interpreted as the states of Markovian environment. We will then determine a system of differential equations for the Laplace-Stieltjes transform of the distribution of discounted aggregate claims under mild assumption. Moreover, using the differentio-integral equation, we will also investigate the first two order moments of discounted aggregate claims in a Markovian environment. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.06.003 |
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