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Only in recent years quantitative analysts have asked for the numerical solution of a free-boundary partial di?erential equation. Fast and accurate numerical algorithms have become essential tools to price ?nancial derivatives and to manage portfolio risks. So far, the emerging ?eld of computational ?nance has hardly been discussed in the mathematical ?nance literature. This book attempts to ?ll the gap. Basic principles of computational ?nance are introduced in a monograph with textbook character.