Dynamic Programming Equation for the Mean Field Optimal Stopping Problem

We study the optimal stopping problem of McKean-Vlasov diffusions when criterion is a function law stopped process. A remarkable new feature in this setting that time also impacts dynamics process through dependence coefficients on law. The mean field introduced weak formulation terms joint marginal underlying and survival This specification satisfies dynamic programming principle. corresponding equation an obstacle Wasserstein space, obtained by means general It\^o formula for flows laws c\`adl\`ag semimartingales. Our verification result characterizes nature policies, highlighting crucial need to randomized stopping. effectiveness our illustrated various examples including mean-variance problem.