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Invariance, Existence and Uniqueness of Solutions of Nonlinear Valuation PDEs and FBSDEs Inclusive of Credit Risk, Collateral and Funding Costs
We study conditions for existence, uniqueness and invariance of the comprehensive nonlinear valuation equations first introduced in Pallavicini et al (2011). These equations take the form of semi-linear PDEs and Forward-Backward Stochastic Differential Equations (FBSDEs). After summarizing the cash flows definitions allowing us to extend valuation to credit risk and …