| On the Expected Discounted Penalty Function for a Risk Process with Stochastic Return on Investments |
| Received:March 21, 2008 Revised:July 04, 2008 |
| Key Words:
expected discounted penalty function integro-differential equation Laplace transform ruin.
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| Fund Project:Supported by Key Project of National Social Science Fund (Grant No.06&ZD039) and ``Mathematics X" Project of DUT. |
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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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