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.
Table of Contents
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 Cramér-Lundberg model
Appendix A: Problems
Appendix B: Bibliographic Remarks
Glossary of Notation
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.
"… a well-chosen collection of topics from risk analysis and management for finance and actuarial science illustrated with solved problems."
—Christel Geiss, Mathematical Reviews, November 2013
Praise for the First Edition:
… a useful addition to a rapidly expanding field.
—Journal of the Royal Statistical Society
Here is a comprehensive and accessible introduction to the ideas, methods and probabilistic models that have transformed risk management into a quantitative science and [have] led to unified methods for analyzing insurance and finance risk.
Risk Analysis in Finance and Insurance is a self-contained and highly comprehensive introduction to mathematical finance and its interplay with insurance risk analysis. Students will like the book due to the many worked-out examples deepening the understanding of the theory. A special and probably unique feature of the book is its unified approach to financial and insurance risks. As a consequence of the convergence of financial and insurance markets, practitioners in financial institutions will have great benefit from books like Melnikov’s covering mathematical approaches to risk analysis in both markets in a consistent manner.
—Christian Bluhm, Credit Suisse, Zurich, Switzerland