带交易费用的最优年金保险购买及投资消费问题

By applying stochastic control theory, this project mainly focuses on the optimization problems in annuity insurance with transaction costs. Our research includes the following main topics: (1) the optimal decision problem when the annuitization takes place under an "anything anytime" annuity model with transaction costs; (2) the optimization problem in life insurance with transaction costs in investment; (3) the optimal annuity purchasing problem with transaction costs in investment. This research proposes a new impulse control problem, and intends to provide, from a different point of view, an explanation for the phenomenon of "annuity puzzle". The anticipated results from this proposed project will not only enrich the research in the area of life insurance, but also promote the development of the stochastic control theory. Moreover, the problem studied in this project is a hot topic concerned by the nation and government, and is also an interdisciplinary research between theoretical theories such as probability, stochastic process, stochastic calculus, and stochastic control, and practical fields such as finance and actuarial science. Hence, the anticipated significance of this research would be the theoretical contributions to the related fields and their practical applications.

本项目拟采用随机控制理论研究带交易费用的年金保险优化问题。主要研究内容包括： (1) 购买带交易费用的"随时购买模式"年金被保人的最优决策问题, (2) 当投资带交易费用时的人寿保险优化问题, (3) 当投资带交易费用时的年金最优购买问题。本项目提出了一个新的脉冲控制问题，希望从一个不同的角度解释"年金延迟现象"可能出现的原因。预期的研究成果将不仅丰富人寿保险领域的研究内容，同时也将促进随机控制理论的发展。本项目所研究的问题是当前国家和政府所关注的热门问题，也是概率论，随机过程，随机分析及随机控制等基础理论与金融，保险精算等应用领域的交叉研究。 因此, 这个研究的预期意义将是对相关领域的理论和它们的实际应用方面的贡献。

老龄化问题是当前国家和政府迫切需要解决的重要问题，购买人寿保险和年金保险是缓解老龄化现状的一个重要手段。本项目主要利用随机最优控制的方法研究人寿保险和年金保险模型中的优化问题。考虑带有交易费用模型下，最优人寿保险或年金保险的购买及投资消费问题； 寿险模型中生命破产概率最小化及相关优化问题。 同时，也研究了非寿险模型中的优化问题及扩散近似问题。研究成果不仅为投资者（或保险公司）购买人寿保险及年金保险（投资，再保险）提供帮助和建议，也促进了随机控制理论的发展。因此，具有一定理论价值和现实意义。