Numerical Methods in Finance

The use of mathematical models and numerical techniques in finance is a growing practice, and an increasing number of applied mathematicians are working on applications in finance and business. This book presents some exciting developments arising from the combination of mathematics, numerical analysis, and finance. It covers a wide range of topics, from portfolio management and asset pricing, to performance, risk, debt and real option evaluation. It also presents applications of a variety of cutting edge approaches and techniques, including robust control, min-max optimisation, Bessel processes, stochastic viability, variational inequalities, and Monte-Carlo test techniques. The book also presents surveys of models and approaches in specific areas in finance, such as corporate debt valuation and portfolio selection.

Résumé
GERAD celebrates this year its 25th anniversary. The Center was created in 1980 by a small group of professors and researchers of HEC Montreal, McGill University and of the Ecole Polytechnique de Montreal. GERAD's activities achieved sufficient scope to justify its conversion in June 1988 into a Joint Research Centre of HEC Montreal, the Ecole Polytechnique de Montreal and McGill University. In 1996, the U- versite du Quebec a Montreal joined these three institutions. GERAD has fifty members (professors), more than twenty research associates and post doctoral students and more than two hundreds master and Ph.D. students. GERAD is a multi-university center and a vital forum for the devel- ment of operations research. Its mission is defined around the following four complementarily objectives: • The original and expert contribution to all research fields in GERAD's area of expertise; • The dissemination of research results in the best scientific outlets as well as in the society in general; • The training of graduate students and post doctoral researchers; • The contribution to the economic community by solving important problems and providing transferable tools.

Contenu

Corporate Debt Valuation: The Structural Approach.- Bessel Processes and Asian Options.- Dynamic Management of Portfolios with Transaction Costs under Tychastic Uncertainty.- The Robust Control Approach to Option Pricing and Interval Models: An Overview.- A Finite Element Method for Two Factor Convertible Bonds.- On Numerical Methods and the Valuation of American Options.- Valuing American Contingent Claims when Time to Maturity is Uncertain.- Foreign Direct Investment: The Incentive to Expropriate and the Cost of Expropriation Risk.- Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions.- A Stochastic Discount Factor-Based Approach for Fixed-Income Mutual Fund Performance Evaluation.- Portfolio Selection with Skewness.- Continuous Min-Max Approach for Single Period Portfolio Selection Problem.