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This paper deals with pricing and hedging based on utility indifference for exponential utility. We consider the limit for vanishing risk aversion or, equivalently, small quantities of the contingent claim. In first order approximation the utility indifference price and the corresponding hedge can be determined from the corresponding quadratic hedging problem relative to the minimal entropy martingale measure. This extends similar results obtained by Mania and Schweizer [21], Becherer [3], and Kramkov and Sîrbu [20,19].

Asymptotic utility-based pricing and hedging for exponential utility