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In this paper, we establish a new proof for the existence and uniqueness of the discrete solution of evolutionary HJB equations which can be approximated by a weakly coupled system of coercive elliptic quasi-variational inequalities (OVIs). For that some properties of the presented algorithm (cf., e.g., Boulaaras and Haiour, 2013; Boulbrachene and Haiour, 2001) using the theta-scheme with respect to the t -variable combined with a finite element spatial approximation are proved. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the parabolic quasi-variational inequalities are transformed into a noncoercive elliptic quasi-variational inequalities. A new iterative discrete algorithm is proposed to show the existence and uniqueness, and a simple proof to asymptotic behavior in uniform norm is also given using the theta time scheme combined with a finite element spatial approximation. The proposed approach stands on a discrete L ∞-stability property with respect to the right-hand side and obstacle defined as an impulse control problem. [Copyright &y& Elsevier]

Abstract A finite element method and implicit time steps are used to determine the price of an American option. The algorithm of Brennan and Schwartz is adapted to this situation and we prove convergence. Numerical tests confirm the theoretical result and lead to a smaller error for the same computational effort, compared to the finite difference method. [ABSTRACT FROM AUTHOR]