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 volume 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, also presenting surveys of models and approaches in specific areas in finance, such as corporate debt valuation and portfolio selection.