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。

youdao

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。

youdao