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.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.