Local Hölder continuity of nonnegative weak solutions of inverse variation-inequality problems of non-divergence type

Compared to the standard variational inequalities, inverse variational inequalities are more suitable for pricing American options with indefinite payoff. This paper investigated the initialboundary value problem of inverse variational inequalities constituted by a class of non-divergence type parabolic operators. We established the existence and Holder continuity of weak solutions. Since the comparison principle in the case of standard variational inequalities is no longer applicable, we constructed an integral inequality using differential inequalities to determine the global upper bound of the solution. By combining it with the continuous method, we obtained the existence of weak solutions. Additionally, by employing truncation factors, we obtained the lower bound of weak solutions in the cylindrical subdomain, thereby obtaining the Holder continuity.