  We consider the problem of maximizing portfolio value when an agent has a
subjective view on asset value which differs from the traded market price. The
agent's trades will have a price impact which affect the price at which the
asset is traded. In addition to the agent's trades affecting the market price,
the agent may change his view on the asset's value if its difference from the
market price persists. We also consider a situation of several agents
interacting and trading simultaneously when they have a subjective view on the
asset value. Two cases of the subjective views of agents are considered, one in
which they all share the same information, and one in which they all have an
individual signal correlated with price innovations. To study the large agent
problem we take a mean-field game approach which remains tractable. After
classifying the mean-field equilibrium we compute the cross-sectional
distribution of agents' inventories and the dependence of price distribution on
the amount of shared information among the agents.
