【作者】 孙万贵；

【导师】 王春峰；

【作者基本信息】 天津大学 ， 管理科学与工程， 2004， 博士

【摘要】 在均值-方差偏好下研究不完全市场中的投资组合问题和或有权的定价、保值问题。一．投资组合问题1．在无摩擦市场和具约束的市场中，证明了二基金强分离，均值-方差有效前沿在均值-标准差空间是一条直线，而且给出了它们的表达式。拟二次效用函数展示了投资组合的均值-方差有效性。同时研究了二市场之间的关系。2．将无摩擦市场中的结论应用于部分信息情况，研究了信息对投资组合的影响。信息不仅影响投资者在无风险资产和风险资产之间的资金分配比例，而且影响风险资产组合。掌握较多信息的投资者的风险资产组合的收益具有较大的期望值和方差，并对应较高的风险价格。引入信息的风险-收益系数的概念。信息的风险-收益系数随信息的增加而增加。在均值-方差偏好意义下投资者的最优收益由其对应信息的风险-收益系数和其风险厌恶参数共同决定。而市场的风险价格完全由信息的风险-收益系数确定。等价信息下最优风险资产组合的收益（在相差常数配意义下）是唯一的，尽管风险资产组合可能不同。零信息下投资者仅投资于无风险资产。投资者对一无所知的风险资产不投资。因此投资者持有某些风险资产（如股票）的比例较高是因为对其它风险资产的信息了解较少。3．卖空机制影响风险资产组合。禁止卖空的股票市场中投资者的最优收益较允许卖空市场具有较小的期望值、方差，并对应较小的风险价格。市场由禁止卖空到允许卖空对投资者来说意味着风险不变时增加收益，或收益给定条件下降低了风险。4．综合考擦卖空机制和部分信息情况，我们得到结论：在确定部分信息下，无论是否允许股票卖空，二基金强分离，均值-方差有效前沿在均值-标准差空间是一条直线。并对不同信息和卖空约束情况，分析了投资者的最优期望收益和风险的差异，研究了风险价格的变化。5．每一部分给出了数值例子。这些例子均为连续时间金融问题，而且发展了已有的数值结果。它们说明，在抽象金融背景下所获结论适应于研究相应的具体金融投资问题。尽管静态投资策略有别于动态策略，本文所获结论既适用于静态投资组合问题，又适用于多期或连续时间投资组合（包括一般或有权的投资组合）问题。二．定价和保值问题研究无摩擦市场中或有权的定价和保值问题，给出了不同标准下或有权的定价公式，并对保值效果进行了分析比较。更多还原

【Abstract】 The optimal portfolios and claim pricing and hedging are addressed under marker incompleteness and mean-variance preferences. On the one hand, the main contents and results on portfolios are as follows:The two-funds strong separation theorem holds and the mean-variance efficient frontier is a straight line in standard deviation-expected return space in the frictionless and constrained financial markets.The results obtained in the frictionless market are applied to study the effects of incomplete information to portfolios. The information affects not only the proportion of capital allocation in the riskless asset to that in risky ones, but also composition of risky assets. The less the information, the lower the expected payoff, risk and the risk price of market.The notion of the payoff-risk coefficient of information is proposed. The payoff-risk coefficient of information increases with the increase of information. The payoff and risk of the optimal risky portfolio is determined by both the payoff-risk coefficient of information and the risk aversion parameter. But the risk price of market is completely dominated by the risk aversion parameter. The payoff of the optimal risky portfolio is unique in the sense of constant times under equivalent information.3. The short-selling mechanism affects the optimal portfolio. The expected mean, the variance and the risk price of the payoff of the risky portfolio without short selling is less than with it. 4. Consider the effects of both information and short-selling mechanism. We conclude that the two-funds strong separation theorem holds and that the mean-variance efficient frontier is a straight line in standard deviation-expected return space under given partial information whether short selling is allowed or not.5. The numeral examples are given at each part.These results apply to static and dynamical portfolio problems although there are differences between them.On the other hand, the claim pricing and hedging are studied in an incomplete <WP=5>market in different criterions. The payoffs in different criterions are given and the performances of them are compared. And using the indifference argument, fair hedging price is derived in a new proof.更多还原