Existence and Uniqueness of Generalized Solutions of Variational Inequalities with Fourth-Order Parabolic Operators in Finance

In the present study, we analyze a kind of variation-inequality problem based on symmetric structure, which also incorporates fourth-order parabolic operators with a degenerate type. The penalty method is used to construct the approximate solution of the variation-inequality problem, and then the existence and uniqueness of the generalized solution are studied by a limit approximation method.