内部信息者的最优效用

Optimal Utility for an Insider

在现有跳扩散模型和对数效用函数的基础上,考虑了内部信息市场中的期望效用最大问题和信息效用比较问题。采用一个到期日可测的随机变量来刻画现实金融市场中处处存在的内部信息,并在此基础上构建了内部信息市场模型,定义了一般信息者和内部信息人士。利用多维跳扩散模型描述风险资产的变化,由此提出两类不同信息投资者的期望效用最大问题。利用扩大信息流方法和随机分析理论,风险资产在内部信息模型下的动态被刻画,两类不同信息者的期望效用最大策略和相应的最大期望效用被明确给出。市场信息影响着投资策略,投资者为获取信息往往需要花费一定的信息成本,不同信息给投资者带来的效用也不相同。在付出信息成本相同的条件下,理性的投资者总会选取能够给自己带来更大效用的信息。为比较信息的效用大小,将不同信息下为得到相同的最大效用而必须投入的初始投资成本之比定义为信息效用比,通过分析给出它的五个性质。最后导出了一般信息与内部信息的效用比的具体表示式。

Based on the current jump-diffusion model and logarithmic utility function,the maximum expected utility problem and information utility comparison problem are considered within an insider information market.A measurable random variable with respect to maturity date is used to describe the insider information in the real financial market.On this basis,the insider information market model is constructed,and the general and the insider are defined.The multi-dimensional jump diffusion model is used to describe risky assets.Based on this model,the expected utility maximization problem of investors with two kinds of different information is put forward clearly.By the initial enlargement of filtration,the problems of expected utility maximization of general and insider,respectively,are solved through stochastic methods and explicit utility maximization strategies and corresponding maximization utilities are formulated respectively.Investment strategies are affected by market information.Investors often need to spend certain information costs to obtain information,and different information brings different effects to investors.Under the assumption of the same information cost,rational investors will always choose the information that can bring them more utility.For the purpose of comparing the utilities of different information,information utility ratio is defined as the ratio of two initials for gaining the equivalent maximized expected utility under different information conditions.Then,its five properties and the ratio of general information to insider information are given explicitly.