2nd Edition

Risk Analysis in Finance and Insurance

By Alexander Melnikov Copyright 2012
    328 Pages 9 B/W Illustrations
    by Chapman & Hall

    328 Pages 9 B/W Illustrations
    by Chapman & Hall

    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.

    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

    Bibliography

    Glossary of Notation

    Index

    Biography

    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.
    Business Horizons

    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