In this paper we consider two cases of optimal implementation delay of taxation with trade-off under spectrally negative Lévy insurance risk processes. In the first case, we assume that the insurance company starts to pay tax only when its surplus level reaches a certain level, and at the termination time of the business there is a terminal value incurred to the company. A method is developed to determine the optimal starting-tax surplus level at which the total expected discounted value of all tax payments up to the termination time plus the discounted terminal value is maximized. In the second case, the company still pays tax subject to a starting-tax surplus level, but with capital injections to prevent bankruptcy. The total expected discounted value of tax payments minus the total discounted capital injection costs is maximized to determine the optimal starting-tax surplus level. Numerical examples are given at the end to illustrate the existence of positive optimal starting-tax surplus levels for both cases considered in this paper.

在本文中，我们考虑了在谱为负的 Lévy 保险风险过程下税收最优实施延迟与权衡的两种情况。在第一种情况下，我们假设保险公司只有在其盈余水平达到一定水平时才开始纳税，并且在业务终止时对公司产生了终值。开发了一种方法来确定最佳起始税收盈余水平，在该水平上，截至终止时间的所有税款的总预期贴现价值加上贴现终值是最大化的。在第二种情况下，公司仍按起始税盈余水平缴纳税款，但注资以防止破产。税收支付的总预期贴现值减去总贴现资本注入成本被最大化以确定最佳起始税盈余水平。最后给出了数值例子来说明本文考虑的两种情况都存在正的最优起始税收盈余水平。