Risk Analysis in Finance and Insurance, Second Edition presents an accessible yet comprehensive introduction to the main concepts and methods that transform risk management into a quantitative science. Taking into account the interdisciplinary nature of risk analysis, the author discusses many important ideas from mathematics, finance, and actuarial science in a simplified manner. He explores the interconnections among these disciplines and encourages readers toward further study of the subject. This edition continues to study risks associated with financial and insurance contracts, using an approach that estimates the value of future payments based on current financial, insurance, and other information.
New to the Second Edition
Expanded section on the foundations of probability and stochastic analysis
Coverage of new topics, including financial markets with stochastic volatility, risk measures, risk-adjusted performance measures, and equity-linked insurance
More worked examples and problems
Reorganized and expanded, this updated book illustrates how to use quantitative methods of stochastic analysis in modern financial mathematics. These methods can be naturally extended and applied in actuarial science, thus leading to unified methods of risk analysis and management.
Alexander Melnikov is a professor in the Department of Mathematical and Statistical Sciences at the University of Alberta. Dr. Melnikov's research interests include mathematical finance and risk management, insurance and actuarial science, statistics and stochastic analysis, and stochastic differential equations and their applications.
Financial Risk Management and Related Mathematical Tools Introductory concepts of the securities market Probabilistic foundations of financial modelling and pricing of contingent claims Elements of probability theory and stochastic analysis Financial Risk Management in the Binomial Model The binomial model of a financial market. Absence of arbitrage, uniqueness of a risk-neutral probability measure, martingale representation Hedging contingent claims in the binomial market model. The Cox-Ross-Rubinstein formula Pricing and hedging American options Utility functions and St. Petersburg's paradox. The problem of optimal investment The term structure of prices, hedging and investment strategies in the Ho-Lee model The transition from the binomial model of a financial market to a continuous model. The Black-Scholes formula and equation Advanced Analysis of Financial Risks: Discrete Time Models Fundamental theorems on arbitrage and completeness. Pricing and hedging contingent claims in complete and incomplete markets The structure of options prices in incomplete markets and in markets with constraints Hedging contingent claims in mean square Gaussian model of a financial market in discrete time. Insurance appreciation and discrete version of the Black-Scholes formula Analysis of Risks: Continuous Time Models The Black-Scholes model. "Greek" parameters in risk management, hedging and optimal investment Beyond the Black-Scholes model Imperfect hedging and risk measures Fixed Income Securities: Modeling and Pricing Elements of deterministic theory of fixed income instruments Stochastic modelling and pricing bonds and their derivatives Implementations of Risk Analysis in Various Areas of Financial Industry Real options: pricing long-term investment projects Technical analysis in risk management Performance measures and their applications Insurance and Reinsurance Risks Modelling risk in insurance and methodologies of premium calculations Risks transfers via reinsurance Elements of traditional life insurance Risk modelling and pricing in innovative life insurance Solvency Problem for an Insurance Company Ruin probability as a measure of solvency of an insurance company Solvency of an insurance company and investment portfolios Solvency problem in a generalized Cramer-Lundberg model Appendix A: Problems Appendix B: Bibliographic Remarks Bibliography Glossary of Notation Index