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Probability and mathematical statistics
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Financial mathematics
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- 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
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- Theory of interest rates
- The basic compound interest functions
- Discounted cash flows
- The valuation of securities an introduction
- Simple stohastic interest rate models
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Stochastic modelling
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Economics
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- 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
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- 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
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Survival models
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Actuarial mathematics I
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- 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
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- 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
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Actuarial mathematics II
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- Decision theory
- Bayesian statistics
- Loss distributions
- Risk models
- Ruin theory
- Credibility theory
- Simple experience rating systems
- Analysis of run-off triangles
- Generalized linear models
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