随机保险模型中的最优分红及风险控制研究

项目名称： 随机保险模型中的最优分红及风险控制研究

项目编号： No.11201352

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 袁海丽

作者单位： 武汉大学

项目金额： 22万元

中文摘要： 本项目拟主要研究随机保险模型中的最优分红及风险控制，具体地（1）具有流动金的随机环境下风险模型的最优红利策略问题：针对常数红利边界策略和门限策略两种不同策略，通过更新方法分析红利现值的期望和矩母函数，并对两种不同红利策略下所得的结果进行分析比较，找出最优的红利策略。（2）具有风险控制的保险风险模型的最优红利策略和最优投资问题：针对VaR限制，CVaR限制，消费限制，财富限制等风险控制下，通过动态规划和鞅方法，找出最优的投资消费策略。项目涉及保险数学、投资组合、风险理论、随机控制理论，风险控制与管理等学科领域，促进了保险数学和金融数学间的交叉研究及相关交叉学科的发展，其成果具有重要理论意义和应用价值,可望应用于保险、金融的风险监控、指导保险机构的投资决策和风险管理。

中文关键词： 风险模型；投资策略；流动金；风险度量；风险控制

英文摘要： This project is designed to study the optimal dividends and risk control about insurance risk model in random environments. This project consists of two parts. (1)we plan to discuss the optimal dividend strategies for insurance risk models in random environments and liquid reserves. Namely, expectations and moment generating functions of discounted dividend payments are analyzed for constant dividend barrier strategy and threshold strategy, respectively. Then, the optimal dividend strategies will be found out.(2)we plan to investigate the optimal dividend and investment strategies for risk models with different risk controls, such as VaR constraint, CVaR constraint，consumption constraint, wealth constraint and so on. The optimal investment consumption strategies are obtained through dynamic programming and martingale method. The project involves several subjects such as insurance mathematics, portfolio selection, risk theory, stochastic control theory, risk control and management. This study will promote a crossover study in insurance mathematics, mathematical finance and related interdisciplinary development. The obtained results are of theoretical significance and application value, and can also be applied to guiding-investment and risk management for insurance institutions and investment corporrations.

英文关键词： risk model；investment strategy；liquid reserve；risk measure；risk control