几类带有loss-carry-forward税收的风险模型的研究

This program studies several risk models with loss-carry-forward taxation. It is the latest topic in the risk theory, but also cross-over study in the risk theory and financial insurance field. With the vigorous development of financial and insurance markets, the risk models established in the research are more close to the actual needs, that is still inadequate, such as the majority of previous models established in the free tax environment. This is one aspect to be improved, and has the good practical significance and research value. To this end, this program studies the following problems: first, we embed loss-carry-forward taxation, investment and loan into the risk model, and consider the absolute ruin probability, the Gerber-Shiu function, the ecpected discounted tax payments, the total duration of the negative surplus and the optimal tax strategy. Second, we study the optimal problem of risk models with loss-carry-forward taxation. By minimizing the risk and maximizing the benefits of the insurance company, we determine the optimal investment and reinsurance strategies, the optimal boundary of collecting taxation and the optimal tax strategy. Third, we investigate the theoretical issues of the piecewise-deterministic Markov process with loss-carry-forward taxation, and discuss relative properties of the ecpected discounted tax payments.

本项目研究带有loss-carry-forward税收的几类风险模型，这是风险理论中的最新课题，也是随机过程理论与金融保险领域的交叉研究。随着金融和保险市场的蓬勃发展，所建立的风险模型也越来越贴近于实际，但仍有不足之处，比如以往建立的模型中大多假定处于无税环境，这是有待完善的地方，具有很好的实际意义与研究价值。为此，本项目研究以下问题：一、将loss-carry-forward税收、投资、贷款因素融入风险模型的构建中，考虑绝对破产概率、Gerber-Shiu函数、期望折现税收、负持续时及最优税收策略；二、研究带有loss-carry-forward税收的风险模型的最优问题，通过最小化公司风险同时最大化其收益，来寻找最优投资和再保险策略，以及最优起始收税边界和最优税收策略；三、研究带有loss-carry-forward税收的逐段决定马尔可夫过程的理论问题，讨论期望折现税收的相关性质。

本项目主要研究了带有loss-carry-forward税收的风险模型，这是风险理论中的最新课题，也是随机过程理论与金融保险领域的交叉研究。我们在该领域的研究中取得了一些进展：目前已有2篇论文正式发表，1篇论文已接收并在线刊出，等待正式发表。本项目研究的是一系列的问题，我们已完成了对带有借款利息和税收的常利率风险模型的研究，计算出了关键的首出时和负持续时的拉普拉斯变换，给出了期望折现税收量的明确表达式；其次，我们研究了一类含借款利率风险过程的负持续时问题，得到了总的负持续时的拉普拉斯变换；此外，我们还考察了一类含常利率的带扰动更新过程，给出了门槛分红策略下该风险过程的期望折现分红量。负持续时的拉普拉斯变换和期望折现分红量是研究税收问题的重要理论基础，这两个结果也为我们继续该项目课题的后续研究提供了技术支撑。

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