2022/2023

Research Seminar "Financial Mathematics"

Category 'Best Course for Career Development'

Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'

Category 'Best Course for New Knowledge and Skills'

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

When: 3, 4 module

Open to: students of all HSE University campuses

Instructors: Mauro Mariani

Language: English

ECTS credits: 6

Contact hours: 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 pricing
  Written exercises, mostly about the mathematical framework that was developed
• Portfolio optimization
• Oral exam
  A discussion over the whole content of the class

Interim Assessment

• 2022/2023 4th module
  0.3 * 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