This paper presents a methodology for characterizing the optimal dynamic behavior of risk-averse, strategic agents with private information, by building on Kyle (Econometrica, 1985, 53, 1315-1335). It is shown that both monopolistic and competing informed traders choose to exploit rents rapidly, causing market depth to be low in the initial periods and high in later periods, and causing information to be revealed rapidly, unlike in the case of a risk-neutral monopolist considered by Kyle.