On the Expected Discounted Penalty Function for a Risk Process with Stochastic Return on Investments
Received:March 21, 2008  Revised:July 04, 2008
Key Word: expected discounted penalty function   integro-differential equation   Laplace transform   ruin.  
Fund ProjectL:Supported by Key Project of National Social Science Fund (Grant No.06&ZD039) and ``Mathematics X" Project of DUT.
Author NameAffiliation
Li Li LI School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Jing Hai FENG School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Li Xin SONG School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
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Abstract:
      This paper considers the expected discounted penalty function $\Phi(u)$ for the perturbed compound Poisson risk model with stochastic return on investments. After presenting an integro-differential equation that the expected discounted penalty function satisfies, the paper derives the closed form solution by constructing an identical equation. The exact expression for $\Phi'(0)$ is given using the Laplace transform technique when interest rate is constant. Applications of the results are given to the ruin probability and moments of the deficit at ruin.
Citation:
DOI:10.3770/j.issn:1000-341X.2010.02.014
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