Abstracts

We discuss the continuous-time utility maximization problem under asymmetric information in financial markets, in the context of Fads models (Shiller, 1981) and signaling theory of trade. Particularly, our work is based on the asset pricing approach introduced by Guasoni (2006), which models price dynamics with both a martingale component and a stationary component. Based on this framework, we formulate a different process for the price dynamics. Whereas Guasoni (2006) models the price dynamics from a GBM and an Ornstein-Uhlenbeck process, our analysis draws on two Ornstein-Uhlenbeck processes. The asset price for the informed agents is in the larger filtration and initially specified. From this we decompose the asset price dynamics of the uninformed agents in the smaller filtration. We find non-Markovian dynamics for the uniformed agents, which requires analysis of the filtering problem by applying the Hitsuda representation (1968). We then solve the logarithmic utility maximization problem, in order to compare both agents' level of market information. In contrast to the method in Guasoni (2006), where the above dynamics are obtained by applying the theory of the negative resolvent of a Volterra kernel to a product function, we start out from the representations of the process, and then verify our solution by using the fundamental equation from the general scheme given in Cheredito (2003). This allows us to confirm the existence of the negative resolvent associated with a Volterra Kernel, which is a sum of functions. Subsequently, by recalling the logarithmic utility maximization problem from the terminal wealth, we obtain the two agents' optimal trading strategies. Our study supports the results of Guasoni (2006), where informed and uninformed agents' log utilities are found to be different. Particularly, our analysis yields positive excess utility for informed agents.