Convergence of Utility Indifference Prices to the Superreplication Price: the Whole Real Line Case

A discrete-time financial market model is considered with a sequence of investors whose preferences are described by concave strictly increasing functions defined on the whole real line. Under suitable conditions we prove that, whenever their absolute risk-aversion tends to infinity, the respective utility indifference prices of a given bounded contingent claim converge to the superreplication price. We also prove that there exists an accumulation point of the optimal strategies’ sequence which is a superhedging strategy.