Abstract
In this paper, we study a class of reflected backward stochastic differential equations (BSDEs) of mean-field type, where the mean-field interaction in terms of the distribution of the Y-component of the solution enters in both the driver and the lower obstacle. We consider in details the case where the lower obstacle is a deterministic function of and discuss the more general dependence on the distribution of 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 convergence of the standard penalization scheme to the solution of the equation, which hence satisfies a minimality property. This class of equations is motivated by applications in pricing life insurance contracts with surrender options.
Funding Statement
The first author gratefully acknowledges the financial support provided by the Swedish Research Council grant (2016-04086).
Citation
Boualem Djehiche. Romuald Elie. Said Hamadène. "Mean-field reflected backward stochastic differential equations." Ann. Appl. Probab. 33 (4) 2493 - 2518, August 2023. https://doi.org/10.1214/20-AAP1657
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