Risk Analysis in Finance and Insurance: 2nd Edition (Paperback) book cover

Risk Analysis in Finance and Insurance

2nd Edition

By Alexander Melnikov

Chapman and Hall/CRC

328 pages | 9 B/W Illus.

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Description

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.

Reviews

"… 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

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

Bibliography

Glossary of Notation

Index

About the Author

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.

Subject Categories

BISAC Subject Codes/Headings:
BUS027000
BUSINESS & ECONOMICS / Finance
MAT000000
MATHEMATICS / General
MAT029000
MATHEMATICS / Probability & Statistics / General