Optimal strategies and utility-based prices converge when agents' preferences do
Résumé
A discrete-time financial market model is considered with a sequence of investors whose preferences are described by utility functions $U_n$ defined on the whole real line. It is shown, under suitable hypotheses, that whenever $U_n$ tends to a utility function $U_{\infty}$, the respective optimal strategies, the Davis and Hodges-Neuberger prices converge, too. Under additional assumptions the rate of convergence can also be estimated.
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