Before revision:  As an application , we study utility indifference valuation of financial derivatives with unbounded payoffs, obtaining a new convex dual representation of the prices and their asymptotics for the risk aversion parameter  .
After revision:  As an application , we study utility indifference valuation of financial derivatives with unbounded payoffs, obtaining a new convex dual representation of the prices and their asymptotics for the risk aversion parameter tends to either zero or infinity .