In the present work we study the solution  existence for a generalized Dynkin game of switching type which is shown to be the natural representation for general defaultable OTC contract in which acontingent CSA has been set between the parties . This is a theoretical counterparty risk mitigation mechanism that allows the counterparty of a general OTC contract to switch from zero to full/perfect collateralization and switch back whenever she wants until contract maturity paying some switching costs and taking into account the running costs that emerge over time. In this paper we allow for the strategic interaction between the counterparties of the underlying contract, which makes the problem solution much more tough. We are motivated in this research by the importance to show the economic sense - in terms of optimal contract design - of a contingent counterparty risk mitigation mechanism like our one. In particular, we show that the existence of the solution and the game Nash equilibrium is connected with the solution of a system of non-linear reflected BSDE which remains an  problem. We have also proved its existence under strong condition ( in the so called \emph{symmetric case ) highlighting in conclusion some interesting applications in finance and future researches .
We study the solution 's existence for a generalized Dynkin game of switching type which is shown to be the natural representation for general defaultable OTC contract with contingent CSA . This is a theoretical counterparty risk mitigation mechanism that allows the counterparty of a general OTC contract to switch from zero to full/perfect collateralization and switch back whenever she wants until contract maturity paying some switching costs and taking into account the running costs that emerge over time. In this paper we allow for the strategic interaction between the counterparties of the underlying contract, which makes the problem solution much more tough. We are motivated in this research by the importance to show the economic sense - in terms of optimal contract design - of a contingent counterparty risk mitigation mechanism like our one. In particular, we show that the existence of the solution and the game Nash equilibrium is connected with the solution of a system of non-linear reflected BSDE which remains an open problem. We then provide the basic ideas to numerically search the game equilibrium via an iterative optimal stopping approach and we show the existence of the solution for our problem under strong condition , in the so called \emph{ symmetric case .
R
In the present work we
We
A
's
D
defaultable OTC contract
D
in which a
D
contingent CSA
R
has been set between the parties
defaultable OTC contract with contingent CSA
R
counterparty risk mitigation mechanism
counterparty risk mitigation mechanism
R
Nash equilibrium
Nash equilibrium
A
open
R
have also proved its existence
then provide the basic ideas to numerically search the game equilibrium via an iterative optimal stopping approach and we show the existence of the solution for our problem
R
(
,
D
symmetric case
R
) highlighting in conclusion some interesting applications in finance and future researches
symmetric case