在带注资的经典风险模型中研究征税问题. 假设税收按照loss-carry-forward制度支付. 当盈余低于0时, 将采取注资的方式使得盈余达到0而不致破产. 利用微分法, 得到了期望折现征税总额减去期望折现注资成本总额($V(x)$)满足的积分-微分方程, 给出了初始盈余趋于无穷时$V(x)$的极限值, 并在指数理赔假设下给出了$V(x)$的显式表达式. 除此之外, 还给出了一个例子.

In this paper, we study the taxation problems in the classical risk model with capital injections. Assume that the taxes are paid according to a loss-carry-forward system. Once the surplus is below 0, we let the surplus attain 0 avoiding ruin by capital injections. Applying the ``differential argument", the integro-differential equation for the total expected discounted tax payments minus the total expected discounted costs of capital injections ($V(x)$) is derived, the limitation of $V(x)$ is given when the initial surplus $x$ tends to infinity, and the explicit expression for $V(x)$ is obtained under the assumption that the claim sizes are exponentially distributed. In addition, an example is presented.