A multidimensional exponential utility indifference pricing model with applications to counterparty risk

This paper considers exponential utility indifference pricing for a multidimensional nontraded 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, whose convergence is proved based on the Barles-Souganidis monotone scheme, and the convergence rate is derived based on Krylov’s shaking the coefficients technique. We apply our methodology to study the counterparty risk of derivatives in incomplete markets