Optimal form & deadline for paying insurance agents their commission

In view of this question, whether lengthening the deadline of commission payment can effectively restrict the occurrence of myopia action of the insurance agent, a long-term principal-agent model and a model of the best deadline of commission payment are established. It´s proved that the optimal insurance contract must have the part of fixed wages. A formula for the best deadline of commission payment is given. Meanwhile the models of the reference and are improved, and also some conclusions of those references are strengthened.