破产终端值影响下保险公司最优分红、注资和溢额再保险策略

Optimal dividend, capital injection and excess-of-loss reinsurance strategies for insurer with a terminal value of the bankruptcy

本文假设保险公司可通过分红、注资和购买溢额再保险三种方式动态地控制盈余过程.同时控制过程会消耗交易费用:再保险合同是"不便宜的";分红需要纳税;而注资需要比例注资成本和固定注资成本.在最大化公司价值目标下,本文给出了最优的控制策略,并分析了交易费用和任意破产终端值的影响.结果表明,当交易费用较低且破产终端值相对较小时,注资可能最优,应当按照Barrier策略进行分红;当公司盈余增加时,应当减少再保险购买量.

In this paper, we assume that an insurance company can control dividend, capital injection and excess-of-loss reinsurance strategies dynamically. Transaction costs are incurred by these business activities：Reinsurance is ＂non-cheap＂, dividend is taxed, reinvestment generates proportional and fixed costs. An arbitrary terminal value of the bankruptcy is considered. Under the objective of maximizing the company＇s value, we present the optimal strategies and analyze the effects of transaction costs and terminal value. The results show that capital injection maybe profitable if transaction costs and terminal value are relatively low, dividends should be paid under the barrier strategy, less reinsurance is bought when the surplus increases.