CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2008, 24(3) 319-326 DOI:      ISSN: 1001-4268 CN: 31-1256

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Keywords
Stochastic premium
integral equation
penalty function
the time of ruin
the deficit at ruin
the surplus immediately before ruin occurs.
Authors
Yao Dingjun
Wang Rongming
Xu Lin
PubMed
Article by
Article by
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On the Expected Discounted Penalty Function Associated with the Time of Ruin for a Risk Model with Random Income

Yao Dingjun, Wang Rongming, Xu Lin

School of Finance and Statistics, East China Normal University; School of Mathematic and Computer Science, Anhui Normal University

Abstract��

This paper studies the expected discounted penalty function associated with the time of ruin for a risk model with stochastic premium. The premium process is no longer a linear function of time in contrast with the classical Cram\'{e}r-Lundberg model. The aggregate premiums constitute a compound Poisson process which is also independent of the claim process. Integral equation for the penalty function is derived, which provides a unified treatment to the ruin quantities. Applications of the integral equation are given to the Laplace transform of the time of ruin, the deficit at ruin, the surplus immediately before ruin occurs. In some special cases with exponential distributions, closed form expressions for these quantities are obtained, which generalize some known results about the problems of ruin in Boikov (2003).

Keywords�� Stochastic premium   integral equation   penalty function   the time of ruin   the deficit at ruin   the surplus immediately before ruin occurs.  
Received 1900-01-01 Revised 1900-01-01 Online:  
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Corresponding Authors: Yao Dingjun
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