Stochastic Financial Mathematics
Teaches: Shportyuk Volodymyr
In the present course doctoral students are introduced to the main theoretical instruments of a financial analytic: objective and risk-neutral probabilities, random walk of market characteristics (geometrical Brownian motion), martingale processes, construction of Ito integral, multi-dimensional stochastic processes, stochastic differential equations, Kolmogorov equations, theories of valuating European, American, and exotic options, Black-Scholes and Merton models, calibration models of Cox–Ingersoll–Ross and Brace Gatarek Musiela etc. The place of stochastic calculus in the work of a financial analytic is the same as the differential calculus does in the work of a qualified engineer.