Reflected Backward SDE approach to the price-hedge of defaultable claims with contingent switching CSA

In this work we study the price-hedge issue for general defaultable contracts characterized by the presence of a contingent CSA of switching type. This is a contingent risk mitigation mechanism that allow the counterparties of a defaultable contract to switch from zero to full/perfect collateralization and switch back whenever until maturity T paying some instantaneous switching costs , taking in account in the picture CVA, collateralization and the funding problem. We have been lead to the stud...