• Fixed-income securities, basic portfolio optimization, binomial method for options; Ito process and its applications in stock market, Black-Scholes equation and its solution; random numbers, transformation of random numbers and generating normal variates, Monte Carlo integration, pricing options by Monte Carlo simulation, variance reduction techniques, quasi-random numbers and quasi-Monte Carlo simulation; introduction to finite difference methods, explicit and implicit finite difference schemes, Crank-Nicolson method, free-boundary value problems for American options.

    For further information see the academic catalog: IAM749

  • The course consists of a detailed description of continuous and discrete dynamical systems. We shall combine the introduction to the general theory with the consideration of bifurcations and chaos, the most important subtopics. The analysis of appropriate mechanical, physical, economic and biological models is an essential part of almost every lecture of the course. To support the course numerical and computational toolbox will be used.

    For further information see the academic catalog: IAM529