Risk Analysis in Finance and Insurance

by Alexander Melnikov

Overview

Risk Analysis in Finance and Insurance, Third Edition presents an accessible yet comprehensive introduction to the main concepts and methods that transform risk management into a quantitative science. Considering the interdisciplinary nature of risk analysis, the author discusses many important ideas from stochastic analysis, mathematical 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.

Features of the third edition

• 12 chapters instead of 8 of the 2^nd edition. Two new chapters on Wiener process as a base for financial market modeling. Option pricing in the Bachelier model, the model of Black and Scholes, the Gram-Charlier model. American options and their pricing in the Black-Scholes model

• Several new notions, topics and results that are not reflected yet in other textbooks, and even in monographs (Binomial model with constraints, detailed exposition of quantile hedging technique, Conditional Value at Risk, Range of Value at Risk, applications to equity-linked life insurance)

• Can be regarded as a self-contained issue of courses on Mathematical Finance, Actuarial Science and Risk Management

• Replete with new exercises, problems, hints and solutions

Product Details

ISBN-13:	9781032395111
Publisher:	CRC Press
Publication date:	09/04/2025
Series:	Chapman and Hall/CRC Financial Mathematics Series
Edition description:	3rd ed.
Pages:	374
Product dimensions:	6.12(w) x 9.19(h) x (d)

About the Author

Alexander Melnikov is a Professor at the University of Alberta working in stochastic analysis and its applications in finance, statistics and insurance. He is the author of nine books and over one hundred research papers in leading academic journals and venues. He is a Fellow of the Russian Academy of Natural Sciences, a recipient of the Leontiev medal of this academy and the McCalla Professorship of the University of Alberta. In addition to his academic engagements, he held several senior positions in business and professional organizations.

Table of Contents

1 Introductory Concepts of Financial Risk Management 2 Financial Risk Management in the Standard Binomial Mode 3 Binomial Model with Constraints and Transition to the Black-Scholes Model 4 Advanced Analysis of Financial Risks in Discrete Time Models 5 Stochastic Analysis in the Context of Financial Mathematics 6 Modelling Markets with Wiener Processes 7 Quantile Hedging Methodology within the Black-Sholes Model 8 Risk Measures as Quantitative Tools of Risk Management 9 Fixed Income Securities: Modelling and Pricing 10 Real and American Options. Performance Measures and Analysis 11 Insurance and Reinsurance Risks 12 Solvency Problem for an Insurance Company 13 Problems Bibliography Glossary of Notation Index

Editorial 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

From the Publisher