Probability Colloqium
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Said Hamadene (Le Mans University)

Mean-field reflected backward stochastic differential equations

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. 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 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.