New existence theorems for quasi-variational inequalities and applications to financial models

The Financial Equilibrium Problem with a Markowitz-Type Memory Term and Adaptive Constraints

“…Now, the feasible set for assets, liabilities and prices is: where α, β and δ are positive parameters to be appropriately fixed. Solving the associated variational inequality with the same technique (see [18]) and…”

“…In order to prove Theorem 2.1, let us recall some definitions and a general existence result (see [18,31]). …”

“…We point out that we are able to derive a quasi-variational formulation of this financial equilibrium problem with memory and adaptive constraints. For the previous papers on the evolutionary financial model, see [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Inverse problems for quasi-variational inequalities

“…The theory of quasi-variational inequalities has now established itself as one of the most promising areas of applied mathematics, offering a powerful mathematical apparatus for investigating a broad range of problems arising in diverse disciplines. Applications of quasivariational inequalities can be found in material science [12], equilibrium models [2,22], financial models [6], frictional elastostatic contact [19], image processing [16], sand-piles formation [3], and numerous others.…”

Cooperation in traffic network problems via evolutionary split variational inequalities

“…Firstly, Daniele et al [19] constructed a time-dependent traffic network equilibrium problem in the terms of an evolutionary variational inequality problem. Several problems related to the economic world, such as spatial price equilibrium problem, internet problem with multiple classes of traffic, Nash equilibrium problem, pollution control problem, dynamic financial and oligopolistic market equilibrium problems have been studied via an evolutionary variational inequality problem in [3,5,6,13,18,30,33].…”