Adaptive Methods For Variational Inequalities

ISBN-13: 9783838384573 / Angielski / Miękka / 2010 / 204 str.

Chen-Song Zhang

Opis

Variational inequalities (VIs) arise from a wide range of application areas, like mechanics, control theory, engineering, and finance. One of the emerging applications of variational inequalities in finance is valuation of American-style options. An option is a derivative contract where the future payoffs to the buyer and seller of the contract are determined by the price of another security, such as a common stock or a basket of stocks. American option pricing can be formulated as an obstacle problem, a particular example of VIs. To solve time dependent variational inequalities numerically, we employ the explicit or implicit Euler method for time-discretization and the finite element method (FEM) for space-discretization with adaptive time-space mesh refinement techniques. Adaptive mesh refinement is an important tool to deal with multiscale phenomena and to reduce the size of the linear systems that arise from the discretization.

O autorze

PhD: Studied numerical optimization at Nanjing University, China and applied mathematics at University of Maryland, College Park, U.S.A. Chowla assistant professor at Penn State University, University Park, U.S.A.