This paper deals with pricing and hedging based on utility indifferences for exponential utility. We consider the limit for vanishing risk aversion or, equivalently, small quanities of the contingent claim. In first order approximation the utility indifference price and the corresponding hedge can be determined from the corresponding quadratic hedgin problem relative to the minimal entropy martingale measure. This extends dimilar results obtained by Mania and Schweizer, Becherer, and Kramkov and Sirbu
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