In this paper we provide a generalization of Feynmac–Kac formula under volatility uncertainty in presence linear term the PDE due to discounting. We state our result different hypothesis with respect derivation given by Hu et al. (2014), where Lipschitz continuity some functionals is assumed which not necessarily satisfied setting. particular, show that G-conditional expectation discounted payo...

We give a generalization of Hochster’s formula for local cohomologies of square-free monomial ideals to monomial ideals, which are not necessarily square-free. Using this formula, we give combinatorial characterizations of generalized Cohen-Macaulay monomial ideals. We also give other applications of the generalized Hochster’s formula.