In this talk, we study a class of reflected backward stochastic differential equations (BSDEs) of mean-field type, where the mean-field interaction in terms of the expected value E[Y ] of the Y-component of the solution enters both the driver and the lower obstacle. We consider the case where the lower obstacle is a deterministic function of (Y, E[Y ]). Under mild Lipschitz and integrability conditions on the coefficients, we obtain the well-posedness of such a class of equations. Under further monotonicity conditions, we show the convergence of the standard penalization scheme to the solution of the equation. This class of models is motivated by applications in pricing life insurance contracts with surrender options.
This is a joint work with BOUALEM DJEHICHE (KTH, STOCKHOLM) AND ROMUALD ELIE, UMLV, MARNE LA VALLÉE, FRANCE.
Short biography of Speaker:
Said Hamadene is a Professor of Mathematics at the University of Le Mans and a member of the “Manceau laboratory of Mathematics”. He works on BSDE, PDEs, Stochastic optimization, and games. He currently supervises two PhD students and an active member of the institute of risk and insurance at the University of Le Mans. See his personal page for more details.