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 CoxRoss-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
3.2 Probability of bankruptcy as a measure of solvency of an insurance company
3.3 Solvency of an insurance company and investment portfolios
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 Crame´rLundberg model
A Software Supplement: Computations in Finance and Insurance