Магистратура
2022/2023
Введение в стохастические дифференциальные уравнения и числовую вероятность
Статус:
Курс по выбору (Стохастическое моделирование в экономике и финансах)
Направление:
38.04.01. Экономика
Где читается:
Факультет экономических наук
Когда читается:
1-й курс, 3 модуль
Формат изучения:
без онлайн-курса
Охват аудитории:
для всех кампусов НИУ ВШЭ
Преподаватели:
Жабир Жан-Франсуа Мехди
Прогр. обучения:
Стохастическое моделирование в экономике и финансах
Язык:
английский
Кредиты:
3
Контактные часы:
54
Course Syllabus
Abstract
This course aims to provide a solid introduction on the conceptual, theoretical and practical aspects of probabilistic numerical methods and the eld of stochastic differential equations (SDEs). A SDE is typically a dynamical system endowing random components that models the evolution over time of particular phenomena subject to uncertainty (for instance the evolution of a nancial asset, risk assessment in insurance policy, . . . ). The course will present the importance of using SDEs to model random phenomenons, from their origin in Physics to their modern applications in Finance, Economy, Machine learning and other eld of Engineering, and surveys in depth the fundamental analytical tools which enables to investigate such models. Along this presentation, general methods to simulate random variables (discrete, real, multivariate), some essential randomized algorithms, and approximation techniques for simulating and investigating fundamental SDEs arising in Finance (e.g. Black and Scholes models, interest rates and bond model) will be reviewed. This course is primarily designed for students possessing a solid background in probability theory and some knowledge and understanding on mathematical modeling, mathematical analysis, differential equations, and computer programming. Although some knowledge on stochastic processes will be useful, part of the course will be dedicated to review/recall the fundamentals of the theory and applications on basic stochastic processes (martingales, Markov processes, Brownian motion) which will be used throughout the course.