By the strong Markov property of the surplus process, we derive the expected discounted penalty function.

利用盈余过程的强马尔可夫性，得到了期望折现罚金函数。

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This paper studies the expected discounted penalty function associated with the time of ruin for a risk model with stochastic premium.

同时，对于本罪中罚金刑的适用及与相关犯罪的区别也应予以充分重视。

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At first, we get the integro-differential equation satisfied by the expected discounted penalty function by using the method of renewal, and hence Laplace transform of it is derived.

首先通过更新论证的方法得到罚金折现期望满足的积分-微分方程，然后推导拉普拉斯变换的表达式，并就索赔额服从指数分布的情形得到了罚金折现期望的精确表达式。

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