Risk Analysis in Finance and Insurance

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