基金定投理论和年金理论中双随机问题的研究-概率论与数理统计专业论文.docxVIP

第 第 PAGE 2 页 共 68 页 申请上海交通大学硕士学位论文 基金定投理论和年金理论中双随机问题的研究 硕士研究生：唐福全 导 师：韩东（教授） 专 业：概率论与数理统计 研究领域：随机过程及其应用 经济和金融数学模型 上海交通大学理学院数学系 A Thesis Submitted to Shanghai Jiao Tong University for the Master’s Degree Study of the dual randomness for automatic investment plan of mutual fund theory and annuity theory Master Candidate: Tang Fuquan Academic Advisor: Prof. Han Dong Major :Probaility and Mathematical Statistics Research Area : Stochastic Process and its Application, Economic and financial mathematics modeling Department of Mathematics Shanghai Jiao Tong University Shanghai, P.R. China 第 第 PAGE 10 页 共 68 页 摘 要 在基金定投投资和支付年金中，利率和持有期限是两个重要的变量，在分 析投资收益和防范风险等方面具有重要作用。本文站在保险公司的角度，假定其 采用基金定投的方式进行资产投资，并有规律的支付年金，通过分析两种行为的 未来现金流的现值，来分析保险公司的收益以及风险程度。 基金定投是以某类基金为投资标的，有规律的购买，并在未来某个时刻集 中赎回。本文提出基金定投收益随机模型，并刻画其相关的数学特征，得到在投 资期限和贴现利率为随机条件下的一些关系和性质。年金的支付是以被保险人存 活为前提条件，而对于未来年金的支出必须考虑贴现利率，本文在假定的基础上， 建立年金双随机模型，并分析其数学特征，重点刻画其风险特性。 由于基金定投和年金作为金融合约而言，具有不同的流动性，因此风险不 同，本文结合近年来对于金融合约风险的刻画，提出了建立在上述两种资产行为 的公司风险模型。 关键词：双随机、基金定投、年金、风险 ABSTRACT Study of the dual randomness for automatic investment plan of mutual fund theory and annuity theory For automatic investment plan (AIP) of mutual fund theory and annuity theory, interest rate and the term of investing or morality are two key random factors and they are very important for calculating and evaluating benefits and risks. In this paper,the present value and the risks of automatic investment plan of mutual fund and annuity have been established for insurance company, which gets profits by AIP and pays for annuity. AIP gets benefits for investors by investing regularly on some special mutual fund and sells off in same time. Here we conduct a dual random model for its benefits and get some mathematical characters. For annuity we also get a model for analysing the amount of paying out with the random factors of interest rates and morality. In this paper, we conduct those models on the side of insurance company for expecting its benefits and payment