具边信息的最优效用及其影响

Optimal Utility with Side Information and its Affect

摘要: 利用测度变换及随机滤波考察了$Q$\,-鞅$\{\wt{\Lambda}_t:=\ep^Q[\Lambda_T|{\cal G}_t]\}$的分解. 然后利用这种分解考察了受随机因素影响的股票价格模型中投资者存在边信息和不存在边信息时的效用问题, 给出了最优效用的一种形式, 从而证明了边信息的影响有限.
- 边信息 /
- 效用优化 /
- 测度变换 /
- 随机滤波
Abstract: We first consider the problem of representation of the $Q$-martingale $\{\wt{\Lambda}_t :=\ep^Q[\Lambda_T|{\cal G}_t]\}$. Then we consider a market of a stock price affected by a stochastic factor, in which there exists a insider who only knows the price information and a side information. We consider his problem of optimal utility for terminal wealth with and without side-information, and obtain a form of optimal terminal wealth in two cases. Finally, we compare these two cases for the logarithmic utility, and analyze the influence of the `side information'.