Mean-field reflected backward stochastic differential equations

Boualem Djehiche; Romuald Elie; Said Hamadène

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arXiv · 1911.06079

Mean-field reflected backward stochastic differential equations

Boualem Djehiche·Romuald Elie·Said Hamadène

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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 $(Y,\E[Y])$ 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.

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BibTeX RIS

Boualem Djehiche, Romuald Elie, Said Hamadène. 2019-11-14. Mean-field reflected backward stochastic differential equations. https://arxiv.org/abs/1911.06079

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