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 U_n, defined on the whole real line and assumed to be strictly concave and increasing. Under suitable hypotheses, it is shown that whenever U_n 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 [Davis, M. H. A. 1997. Option pricing in incomplete markets. M. A. H. Dempster, S. R. Pliska, eds. Mathematics of Derivative Securities. Cambridge University Press, pp. 216–226] and the utility indifference price of Hodges and Neuberger [Hodges, R., K. Neuberger. 1989. Optimal replication of contingent claims under transaction costs. Rev. Futures Markets8 222–239] with respect to changes in agents’ preferences.