English > Courses > First year

Postgraduate specialist study in Actuarial mathematics

First year

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 two-state 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 run-off triangles
• Generalized linear models