2022/2023
Научно-исследовательский семинар "Финансовая математика"
Лучший по критерию «Полезность курса для Вашей будущей карьеры»
Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»
Лучший по критерию «Новизна полученных знаний»
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Когда читается:
3, 4 модуль
Охват аудитории:
для всех кампусов НИУ ВШЭ
Преподаватели:
Мариани Мауро
Язык:
английский
Кредиты:
6
Контактные часы:
72
Course Syllabus
Abstract
Methods of financial mathematics are widely used in all areas of economic activities. A deep
understanding of the basics of mathematical modeling of finance is necessary in order to offer new financial
products, control financial risks and give realistic assessments of market conditions. The course will trace the
main stages in the development of financial mathematics, starting with classical arbitrage and pricing theories
to risk management and random volatility models. The presentation will not assume any prior knowledge of
finance.
Learning Objectives
- The goal is to master the main mathematical tools of Mathematical Finance, as well as knowing some classical and modern model where the models are applied. A special focus is given to tools that are used in contemporary applications.
Expected Learning Outcomes
- • Ability to work with the Black-Scholes option pricing model: applicability for the definition of the price and risks of options, as well as its resulted from the underlying assumptions inability to accurately describe the real-world market processes without some amendments.
- A student is aware of the mathematical formalism of stochastic processes and integration
- A student can model financial markets as random processes, and identify its main features.
- Be able to solve optimal control problem. Identify what problems can be solved numerically.
- Be able to compare different approaches to explain similar results in pricing and optimization problems
Course Contents
- Introduction to problems and tools of Financial Mathematics
- Stochastic Processes and Stochastic Integration
- Markets and Stochastic Dynamics
- Pricing Problems
- Optimal control and decision processes
- Comparisons and asymptotic of optimality and pricing formulas
Assessment Elements
- Stochastic models and pricingWritten exercises, mostly about the mathematical framework that was developed
- Portfolio optimization
- Oral examA discussion over the whole content of the class
Interim Assessment
- 2022/2023 4th module0.3 * Stochastic models and pricing + 0.4 * Oral exam + 0.3 * Portfolio optimization
Bibliography
Recommended Core Bibliography
- Markov decision processes with applications to finance, Bauerle, N., 2011
- Stochastic differential equations : an introduction with applications, Oksendal, B., 1998
- Основы стохастической финансовой математике. Т.2: Теория, Ширяев А.Н., 2004
Recommended Additional Bibliography
- Introduction to stochastic calculus applied to finance, Lamberton, D. M., 2008
- Stochastic integration and differential equations, Protter, P. E., 2005
- Основы стохастической финансовой математики. Т. 1: Факты. Модели, Ширяев, А. Н., 1998