Probability and mathematical statistics

Financial mathematics

 Descriptive analysis of data
 Random variables
 Generating functions
 Joint distributions of random variables
 Central limit theorem and applications
 Sampling and statistical inference
 Point estimation
 Confidence intervals (CI)
 Testing statistical hypothesis
 Correlation and regression analysis
 Analysis of variance
 Conditional expectation

 Theory of interest rates
 The basic compound interest functions
 Discounted cash flows
 The valuation of securities an introduction
 Simple stohastic interest rate models

Stochastic modelling

Economics

 Model structure and the principles of actuarial modelling
 Stochastic processes: definition and classification
 Markov chains
 Markov jump procesess
 Time series analysis
 Brownian motion and diffusions
 Monte Carlo simulation of stochastic processes
 Process of actuarial modelling

 Supply and demand, price equilibrium
 Elasticity of supply and demand
 Utility theory and consumer choice
 National economy
 Public sector finance
 Keynesian model
 Monetary politics
 Government macroeconomics policy

Survival models

Actuarial mathematics I

 Survival models and the life table
 Estimating the lifetime distribution
 The twostate Markov model
 The general Markov model
 Binomial and Poisson models
 Graduation and statistical tests
 Methods of graduation
 Exposed to risk
 Heterogeneity within population and selection
 The evaluation of assurances and annuities
 Premiums and reserves

 Straightforward functions involving two lives
 Use of straightforward functions involving selection
 Variable benefit, disability and long term care contracts
 Expenses and bonuses of life insurance contracts
 Gross premiums and reserves for fixed and variable benefit contracts
 The technique of discounted emerging costs
 The technique of asset shares in the context of life insurance contracts
 Alterations to contracts
 Costs of guarantees under life insurance contracts
 Mortality; selection and standardization
 The process of population projection and its main determinants
 Valuation of benefits under a disability insurance contract

Actuarial mathematics II
 
 Decision theory
 Bayesian statistics
 Loss distributions
 Risk models
 Ruin theory
 Credibility theory
 Simple experience rating systems
 Analysis of runoff triangles
 Generalized linear models

