Risk Analysis in Finance and Insurance

ALEXANDER MELNIKOV

Chapman & Hall

Contents

1 Foundations of Financial Risk Management
1.1 Introductory concepts of the securities market. Subject of nancial
mathematics
1.2 Probabilistic foundations of nancial modelling and pricing of contingent
claims
1.3 The binomial model of a nancial market. Absence of arbitrage,
uniqueness of a risk-neutral probability measure, martingale representation.
1.4 Hedging contingent claims in the binomial market model. The Cox-
Ross-Rubinstein formula. Forwards and futures.
1.5 Pricing and hedging American options
1.6 Utility functions and St. Petersburg’s paradox. The problem of optimal
investment.
1.7 The term structure of prices, hedging and investment strategies in the
Ho-Lee model
2 Advanced Analysis of Financial Risks
2.1 Fundamental theorems on arbitrage and completeness. Pricing and
hedging contingent claims in complete and incomplete markets.
2.2 The structure of options prices in incomplete markets and in markets
with constraints. Options-based investment strategies.
2.3 Hedging contingent claims in mean square
2.4 Gaussian model of a nancial market and pricing in exible insurance
models. Discrete version of the Black-Scholes formula.
2.5 The transition from the binomial model of a nancial market to a
continuous model. The Black-Scholes formula and equation.
2.6 The Black-Scholes model. ‘Greek’ parameters in risk management,
hedging under dividends and budget constraints. Optimal investment.
2.7 Assets with xed income
2.8 Real options: pricing long-term investment projects
2.9 Technical analysis in risk management
3 Insurance Risks. Foundations of Actuarial Analysis
3.1 Modelling risk in insurance and methodologies of premium calculations
© 2004 CRC Press LLC
3.2 Probability of bankruptcy as a measure of solvency of an insurance
company
3.2.1 Cram´er-Lundberg model
3.2.2 Mathematical appendix 1
3.2.3 Mathematical appendix 2
3.2.4 Mathematical appendix 3
3.2.5 Mathematical appendix 4
3.3 Solvency of an insurance company and investment portfolios
3.3.1 Mathematical appendix 5
3.4 Risks in traditional and innovative methods in life insurance
3.5 Reinsurance risks
3.6 Extended analysis of insurance risks in a generalized Cram´er-
Lundberg model
A Software Supplement: Computations in Finance and Insurance
B Problems and Solutions
B.1 Problems for Chapter 1
B.2 Problems for Chapter 2
B.3 Problems for Chapter 3
C Bibliographic Remark
References
Glossary of Notation