过滤的Shannon信息与局内人的附加对数效用
The Shannon information of filtrations and the additional logarithmic utility of insiders
摘要：
本文研究的效用与信息论之间的一般数学联系的背景是一个简单的金融市场模型，模型中有两类小交易者：不太知情的交易者和内部人，他们的额外信息由其他代理人的过滤放大来表示。预期对数效用增量，即内部人和不太知情的交易者的预期对数效用的差异，是用信息漂移来描述的，也就是说，为了从内部人的角度将价格动态视为鞅，必须消除漂移。一方面，我们描述的信息漂移在一个非常一般的设置自然量表达的概率更好地了解世界。另一方面，这使我们能够通过从信息论中已知的熵相关量来识别附加效用。特别地，在一个完全市场中，内部人在整个交易区间内拥有固定的额外信息，其效用增量可以用其额外知识的香农信息来表示。对于一般的市场，在一些特殊的例子中，我们提供了最大效用的信息不等式的估计。
英文摘要：
The background for the general mathematical link between utility and information theory investigated in this paper is a simple financial market model with two kinds of small traders: less informed traders and insiders, whose extra information is represented by an enlargement of the other agents' filtration. The expected logarithmic utility increment, that is, the difference of the insider's and the less informed trader's expected logarithmic utility is described in terms of the information drift, that is, the drift one has to eliminate in order to perceive the price dynamics as a martingale from the insider's perspective. On the one hand, we describe the information drift in a very general setting by natural quantities expressing the probabilistic better informed view of the world. This, on the other hand, allows us to identify the additional utility by entropy related quantities known from information theory. In particular, in a complete market in which the insider has some fixed additional information during the entire trading interval, its utility increment can be represented by the Shannon information of his extra knowledge. For general markets, and in some particular examples, we provide estimates of maximal utility by information inequalities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
