Master 2024/2025

Introduction to Financial Mathematics

Type: Elective course (Stochastic Modeling in Economics and Finance)

Area of studies: Economics

Delivered by: Laboratory of Stochastic Analysis and its Applications

Where: Faculty of Economic Sciences

When: 2 year, 1 module

Mode of studies: offline

Open to: students of all HSE University campuses

Instructors: Vasili Kolokoltsov

Master’s programme: Stochastic Modelling in Economics and Finance

Language: English

ECTS credits: 3

Course Syllabus

Abstract

Methods of financial mathematics have found wide application in all areas of economic and financial activities of enterprises, banks and other financial organizations. A deep understanding of foundations of mathematical modeling of finances is necessary in order to offer new financial products, control financial risks and provide realistic assessments of market conditions. The roots of financial mathematics came from Bachelier (early 20th century) and Samuelson (mid-20th century). However, the true development of modern financial mathematics, based on the profound results of probability theory and modelling market dynamics, takes its origin from the famous work of Black-Scholes (1973) on estimating the fair price of European options. The course will trace the main stages in the development of financial mathematics, from classical stationary models (Markowitz’s portfolios) to the most modern problematics (limit order book).Reflecting the title "Introduction", the presentation will not assume any prior knowledge of finances. It will present the most fundamental results that can be obtained without using the most technical tools of modern stochastic analysis (i.e. without stochastic differential equations).