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Stochastic Models in Finance and Insurance

The seminar in Czech language has been already open.
The seminar in English language will be agreed later during the year.

Section 1: Stochastic Processes in Finance and Insurance

Presenter: RNDr. Milan Sitař

  • Discrete time Markov chains: Absorbing chains, Irreducible chains. Markov chains with rewards.
  • Continuous time Markov processes: Poisson process. Birth and Death processes. Renewal processes.
  • Diffusion processes: (geometric) Brownian motion. Exponential Lévy process. Ornstein-Uhlenbeck process.
  • Martingales. Principles of stochastic calculus: Stochastic differential equations. Ito’s lemma.
  • Case studies: Credit rating dynamics. Random walk. Bonus/malus system. Risky asset price dynamics. Mean-reversion models of interest rate.

Section 2: Insurance Models

Presenter: RNDr. Milan Sitař

  • Number of survivals. Portfolio evolution. Population models.
  • Bonus/malus system.
  • Frequency and severity models: Number of claims. Individual vs. Collective model. Risk measures.
  • Premium setting. Valuation vs. Market provisions.

Section 3: Financial Models

Presenter: Ing. Kamil Kladívko, Ph.D.

  • Basics of no-arbitrage dynamic asset pricing
o Black and Scholes framework. Self-financing portfolio and payoff replication. Hedging and Greeks.
o Risk-neutral and real-world measures. Market completeness. Fundamental theorems of asset pricing.
  • Interest rate models: Vasicek, Hull and White, CIR, HJM framework. Calibration to market data
  • Option valuation: European, American, Asian, Barrier. Binomial trees.
  • Additional topics: Inflation (index) linked instruments. Incomplete markets.

 

 

Section 4: Monte Carlo Methods

Presenter: RNDr. Milan Sitař

  • Mathematical background: Strong law of large numbers. Central limit theorem.
  • Random number generation: Discrete random variable. Continuous (uniform/nonuniform) random variable. Random vector/matrix.
  • Variance reduction method: Antithetic variable methods. Control variate methods.
  • Case studies: Best estimate of liabilities. Contractual and financial options and guarantees. Simulations of risks.
   
 
   
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