Contemporary finance and actuarial calculations have become so mathematically complex that a rigorous exposition is required for an accurate and complete presentation. This volume delivers just that. It gives a comprehensive and up-to-date methodology for financial pricing and modelling. Also included are special cases useful for practical applications. Beyond the traditional areas of hedging and investment on complete markets (the Black-Scholes and Cox-Ross-Rubinstein models), the book includes topics that are not currently available in monograph form, such as incomplete markets, markets with constraints, imperfect forms of hedging, and the convergence of calculations in finance and insurance. The book is geared toward specialists in finance and actuarial mathematics, practitioners in the financial and insurance business, students, and post-docs in corresponding areas of study. Readers should have a foundation in probability theory, random processes, and mathematical statistics.
Financial systems: Innovations and the risk calculus Random processes and the stochastic calculus Hedging and investment in complete markets Hedging and incomplete markets Markets with structural constraints and transaction costs Imperfect forms of hedging Dynamic contingent claims and American options Analysis of "bond" contingent claims Economics of insurance and finance: Convergence of quantitative methods of calculations Bibliographical notes Bibliography Subject index.