Using the elements from the theory of quadratic backward stochastic differential equations with unbounded terminal data , we solve an exponential utility maximization problem with unbounded random endowments under portfolio constraints. Our results thus generalize the previous results of Hu et al. (2005) [Ann. Appl. Probab., 15, 1691--1712] from bounded to unbounded case. 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  .
We solve an exponential utility maximization problem with unbounded payoffs and portfolio constraints, via the theory of quadratic backward stochastic differential equations with unbounded terminal data . This generalizes the previous work of Hu et al. (2005) [Ann. Appl. Probab., 15, 1691--1712] from the bounded to an unbounded framework. Furthermore , we study utility indifference valuation of financial derivatives with unbounded payoffs, and derive a novel convex dual representation of the prices . In particular, we obtain new asymptotic behavior as the risk aversion parameter tends to either zero or infinity .
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Using the elements from the
We solve an exponential utility maximization problem with unbounded payoffs and portfolio constraints, via the
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, we solve an exponential utility maximization problem with unbounded random endowments under portfolio constraints. Our results thus generalize the previous results
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bounded to unbounded case. As an application
the bounded to an unbounded framework. Furthermore
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obtaining a new
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and their asymptotics for
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tends to either zero or infinity