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We study the solution's existence for a generalized Dynkin game of switchingtype which is shown to be the natural representation for general defaultableOTC contract with contingent CSA. This is a theoretical counterparty riskmitigation mechanism that allows the counterparty of a general OTC contract toswitch from zero to full/perfect collateralization and switch back whenever shewants until contract maturity paying some switching costs and taking intoaccount the running costs that emerge over time. In this paper we allow for thestrategic interaction between the counterparties of the underlying contract,which makes the problem solution much more tough. We are motivated in thisresearch by the importance to show the economic sense - in terms of optimalcontract design - of a contingent counterparty risk mitigation mechanism likeour one. In particular, we show that the existence of the solution and the gameNash equilibrium is connected with the solution of a system of non-linearreflected BSDE which remains an open problem. We then provide the basic ideasto numerically search the game equilibrium via an iterative optimal stoppingapproach and we show the existence of the solution for our problem under strongcondition, in the so called symmetric case.

Generalized Dynkin game of switching type representation for defaultable claims in presence of contingent CSA