Contributed Session Wed.3.MA 313

Wednesday, 15:15 - 16:45 h, Room: MA 313

Cluster 3: Complementarity & variational inequalities [...]

Applications of complementarity


Chair: Wen Chen



Wednesday, 15:15 - 15:40 h, Room: MA 313, Talk 1

Jong-Shi Pang
On differential linear-quadratic Nash games with mixed state-control constraints

Coauthor: Dane Schiro


This paper addresses the class of open-loop differential linear-quadratic Nash games with mixed state-control constraints. A sufficient condition is provided under which such a game is equivalent to a certain concatenated linear-quadratic optimal control problem. This equivalent formulation facilitates the application of a time-stepping algorithm whose convergence to a continuous-time Nash equilibrium trajectory of the game can be established under certain conditions. Another instance of this game is also analyzed for which a convergent distributed algorithm can be applied to compute a continuous-time equilibrium solution.



Wednesday, 15:45 - 16:10 h, Room: MA 313, Talk 2

Vadim Ivanovich Shmyrev
A polyhedral complementarity algorithm for searching an equilibrium in the linear production-exchange model.


A finite algorithm for searching an equilibrium in a linear
production-exchange model will be presented. The algorithm is based on the consideration of two dual polyhedral complexes associating with the model.The intersection point of two corresponding each other polyhedrons of the complexes yields equilibrium prices.Thus, we deal with polyhedral complementarity.
The mentioned approach made it possible to propose also finite
algorithms for some other modifications of the exchange model. These algorithms can be considered as analogues of the simplex method of linear programming.



Wednesday, 16:15 - 16:40 h, Room: MA 313, Talk 3

Wen Chen
A power penalty method for fractional Black-Scholes equations governing American option pricing

Coauthor: Song Wang


In this talk, we present a power penalty approach to the linear fractional differential complementarity problem arising from pricing American options under a geometric Levy process. The problem is first reformulated as a variational inequality, and the variational inequality is then approximated by a nonlinear fractional partial differential equation (fPDE) containing a power penalty term. We will show that the solution to the penalty fPDE converges to that of the variational inequality problem with an exponential order. A finite difference method is proposed for solving the penalty nonlinear fPDE. Numerical results will be presented to illustrate the theoretical findings and to show the effectiveness and usefulness of the methods.


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