Optimal Strategies and Utility-Based Prices Converge When Agents’ Preferences Do

摘要

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 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 Markets 8 222–239 with respect to changes in agents’ preferences.