This paper considers exponential utility indifference pricing for a multidimensional non-traded assets model and provides two approximations for the utility indifference price : a linear approximation by Picard iteration and a semigroup approximation by splitting techniques . The key tool is the probabilistic representation for the utility indifference price by the solution of fully coupled linear forward-backward stochastic differential equations . We apply our methodology to study the counterparty risk of derivatives in incomplete markets.
This paper considers exponential utility indifference pricing for a multidimensional non-traded assets model subject to inter-temporal default risk, and provides a semigroup approximation for the utility indifference price . The key tool is the splitting method . We apply our methodology to study the counterparty risk of derivatives in incomplete markets.
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and provides two approximations
subject to inter-temporal default risk, and provides a semigroup approximation
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: a linear approximation by Picard iteration and a semigroup approximation by splitting techniques
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probabilistic representation for the utility indifference price by the solution of fully coupled linear forward-backward stochastic differential equations
splitting method