2019/11/14 by Boualem Djehiche, Romuald Élie, Djehiche, Boualem +3
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1911.06079
openalex publication_date 2019/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.