Utility Indifference Pricing in an Incomplete Market Model with Incomplete Information

In this article, we consider a derivative pricing model for the stochastic volatility model under an incomplete information. The incomplete information in our works, supposes that the true value of the drift for the stock price process is a random variable, investors only have an information of its distribution. This is more practical financial market than the situation with knowledge of the drift. There are many studies about the dynamic portfolio optimization problem under the incomplete information. In that situation, the corresponding problem becomes a easy to treat by Separating Principle and Bayesian updating formula. We apply these arguments to the utility indifference price approach, and present pricing method taken into account the incomplete information. On the other hand, Sircar and Zariphopoulou (2005) gives bounds and asymptotic approximations for the indifference prices in the stochastic volatility model. In them works, bounds include the drift parameter for the underlying price process. However, in practice, it is able to observe the drift parameter by estimation only. Therefore, it is meaningful to extended to the incomplete information. We derive bounds for the indifference prices using estimated drift, and the relationship between the buyerfs indifference price and the sellerfs one.