The Value of Information under Partial Information for Exponential Utility

The paper investigates the value of information to an investor under the partial information setting for exponential utility. The only information available to the investor is the one generated by the asset price processes and, in particular, the underlying appreciation rate of the risky asset cannot be observed directly. Filtering theory is used to find a filtered estimate of the underlying appreciation rate. This brings about two maximisation problems from which we determine the optimal expected utilities of wealth under partial and full information, via Hamilton-Jacobi-Bellman equations. The value of information is, therefore, calculated as the di↵erence between the two optimal expected utilities. The e↵ect of parameter changes on the value of information is determined by carrying out numerical simulations.