Historically, financial and insurance risks were separate subjects most often analyzed using qualitative methods. The development of quantitative methods based on stochastic analysis is an important achievement of modern financial mathematics, one that can naturally be extended and applied in actuarial mathematics.
Risk Analysis in Finance and Insurance offers the first comprehensive and accessible introduction to the ideas, methods, and probabilistic models that have transformed risk management into a quantitative science and led to unified methods for analyzing insurance and finance risks. The author's approach is based on a methodology for estimating the present value of future payments given current financial, insurance, and other information, which leads to proper, practical definitions of the price of a financial contract, the premium for an insurance policy, and the reserve of an insurance company.
Self-contained and full of exercises and worked examples, Risk Analysis in Finance and Insurance serves equally well as a text for courses in financial and actuarial mathematics and as a valuable reference for financial analysts and actuaries. Ancillary electronic materials will be available for download from the publisher's Web site.
Table of ContentsFOUNDATIONS OF FINANCIAL RISK MANAGEMENT
Introductory Concepts of the Securities Market. Subject of Financial Mathematics
Probabilistic Foundations of Financial Modelling and Pricing of Contingent Claims
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. Forwards and Futures
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
ADVANCED ANALYSIS OF FINANCIAL RISKS
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. Options-Based Investment Strategies .
Hedging Contingent Claims in Mean Square
Gaussian Model of a Financial Market and Pricing in Flexible Insurance Models. Discrete Version of the Black-Scholes Formula .
The Transition from the Binomial Model of a Financial Market to a Continuous Model. The Black-Scholes Formula and Equation.
The Black-Scholes Model. "Greek" Parameters in Risk Management. Hedging under Dividends and Budget Constraints. Optimal Investment
Assets with Fixed Income
Real options: Pricing Long-Term Investment Projects
Technical Analysis in Risk Management
INSURANCE RISKS. FOUNDATIONS OF ACTUARIAL ANALYSIS
Modelling Risk in Insurance and Methodologies of Premium Calculations
Probability of Bankruptcy as a Measure of Solvency of an Insurance Company
Solvency of an Insurance Company and Investment Portfolios
Risks in Traditional and Innovative Methods in Life Insurance
Extended Analysis of Insurance Risks in a Generalized Cram´er-Lundberg Model
Software Supplement: Computations in Finance And Insurance
Problems and Solutions
Glossary of Notation