Adaptive Methods For Variational Inequalities
Autor: | Zhang, Chen-Song |
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EAN: | 9783838384573 |
Sachgruppe: | Mathematik |
Sprache: | Englisch |
Seitenzahl: | 204 |
Produktart: | Kartoniert / Broschiert |
Veröffentlichungsdatum: | 19.07.2010 |
Untertitel: | Theory And Applications In Option Pricing |
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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.