Optimal strategies and utility-based prices converge when agents' preferences do

A discrete–time financial market model is considered with a sequence of investors whose preferences are described by their utility functions Un, defined on the whole real line and assumed to be strictly concave and increasing. Under suitable hypotheses, it is shown that whenever Un tends to another utility function U∞, the respective optimal strategies converge, too. Under additional assumptions the rate of convergence is estimated. We also establish the continuity of the fair price of Davis (1997) and the utility indifference price of Hodges and Neuberger (1989) with respect to changes in agents' preferences.