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Financial Mathematics - Кафедра фінансів НаУКМА
Україна, 04655, м. Київ, вул. Г. Сковороди, 2 корпус 6, кім. 410, тел.(044)425-60-42, 425-77-37 (факс)

Invest in your future with the Master Program of Finance of Kyiv Mohyla Academy!

Master’s Program in Finance is a unique combination of thorough academic education and relevant experience of Ukrainian and European experts. No matter how you see your future: in the scientific field, or in the leading global or local companies, our master's program will give you the self-confidence and your managers or employers will be pleasantly surprised by the level of your preparation and competence.

We do not give all the ready answers, but we give you the opportunity to make your discoveries in a friendly atmosphere and improve your leadership skills. We do not teach you how to think, but we will show you how to transform knowledge and experience to success.

Financial Mathematics

Teaches: Shportyuk Volodymyr

Course Schedule

Theme 1. Fundamentals of the Theory of Sets and Mathematical Logics. Logics of Predicates. Complex Numerals as The Broadening of Real Numbers.

Theme 2. Broadening of the Function Concept. Mapping. Metric and normalized Space. Equivalent Metrics and Norms. Convergence. Limit of a Function.

Theme 3. Main Classes of Sets. Rings, Algebras. Σ-rings, Σ-algebras. Monotonous Classes. Resulted Classes of Sets.


Theme 4. Functions of Sets and Limits. Probability Limits.

Theme 5. Functions of Random Argument.

Theme 6. Algebras Resulted From Sets or Events. Measurable Sets. Indicators of Sets. Algebras Resulted from Random Events. Conditional Mathematical Expectations.

Theme 7. Discrete Multivariable Random Events.

Theme 8. Continuous Multivariable Random Events.

Theme 9. Random Processes. Markov Processes with Discrete Time and Discrete Status.

Theme 10.Ergodic Markov’s Chains.

Theme 11. Markov Processes with Continuous Status. Kolmogorov-Chapmen System of Equations.


  1. Angel de la Fuente Mathematical Methods and Models for Economists Cambridge University Press, 2000.
  2. Bobyk O.I. Beregova G.I., Kopytko B.I. Theory of Probabilities and Mathematical Statistics. Kyiv, 2007.
  3. Dorogovtsev A.Y. Elements of a General Theory of Limits and Integral. Kyiv: Vushcha Shkola, 1989.
  4. Efe A. Ok Real Analysis with Economic Applications., Princeton University Press, 2007, 664 pp.
  5. Efe A. Ok Probability Theory with Economic Applications (http://homepages.nyu.edu/~eo1/books.html).
  6. Karlin and H. M. Taylor. A First Course in Stochastic Processes. 2nd ed. Academic Press, 1975.
  7. Karlin and H. M. Taylor. A Second Course in Stochastic Processes. Academic Press, 1981.
  8. Karlin and H. M. Taylor. An Introduction to Stochastic Modeling, Third Edition. Academic Press, 1998.
  9. Karlin. Mathematical Methods and Theory in Games, Programming, and Economics. Dover Publications, 1992. ISBN 978-0486670201.
  10. Sheftel Z.G. Theory of Probabilities. Kyiv: Vyshcha Shkola, 1994
  11. Shreve, Steven E. Stochastic Calculus for Finance I. The Binomial Asset Pricing Model Series: Springer Finance 2005, XVI, 187 p. ISBN: 978-0-387-24968-1
  12. Shreve, Steven E. Stochastic Calculus for Finance II. Continuous-Time Models Series: Springer Finance. 2nd printing, 2004, XIX, 550 p., ISBN: 978-0-387-40101-0
  13. Sokolov G.A., Chistiakova N.A. Controlled Markov’s Chains in Economics. Moscow: PH Fizmathlit, 2005.
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