Master
2024/2025
Stochastic control in finance
Type:
Elective course (Stochastic Modeling in Economics and Finance)
Area of studies:
Economics
Delivered by:
Department of Statistics and Data Analysis
Where:
Faculty of Economic Sciences
When:
2 year, 3 module
Mode of studies:
offline
Open to:
students of all HSE University campuses
Instructors:
Harold A. Moreno-Franco
Master’s programme:
Stochastic Modelling in Economics and Finance
Language:
English
ECTS credits:
3
Course Syllabus
Abstract
The objective of this course is to provide a comprehensive introduction to Stochastic Control Theory. We will systematically explore various aspects of solving stochastic optimization problems, both in discrete and continuous time, with a strong emphasis on applications in finance and insurance.
In the continuous time framework, the value function associated with these problems is intricately connected to a non-linear partial differential equation known as the Hamilton-Jacobi-Bellman equation. Therefore, we will cover essential mathematical tools that will facilitate our understanding of this critical relationship.
By the end of the course, students should be well-equipped to approach stochastic optimization problems methodically and apply their knowledge to relevant fields effectively.
Course Prerequisites: Students are expected to have a mathematical background equivalent to that of the first year of our master’s program in 'Stochastic Modeling in Economics and Finance'. This includes a solid foundation in Probability Theory and Stochastic Differential Equations.
Learning Objectives
- Understand Fundamental Concepts: Develop a clear understanding of the key concepts and principles within Stochastic Control Theory, including stochastic processes, dynamic programming, and optimization.
- Apply Stochastic Optimization Techniques: Learn to formulate and solve stochastic optimization problems in both discrete and continuous time settings, particularly in the context of financial and insurance applications.
- Analyze the Hamilton-Jacobi-Bellman Equation: Gain proficiency in the Hamilton-Jacobi-Bellman (HJB) equation, recognizing its significance as it relates to the value function in continuous time stochastic control problems.
- Utilize Mathematical Tools: Familiarize yourself with essential mathematical tools and techniques, such as dynamic programming principles and Itô calculus that are pivotal in solving and analyzing stochastic control problems.
- Implement Real-World Applications: Explore various real-world applications of Stochastic Control Theory, particularly in finance and insurance, highlighting how these theoretical concepts can be applied to practical scenarios.
- Evaluate and Compare Solutions: Develop skills to critically evaluate different solution methods and compare their effectiveness in addressing stochastic optimization challenges.
- Conduct Independent Research: Encourage the pursuit of independent research or projects that utilize Stochastic Control Theory to tackle complex problems in economics and finance.
Expected Learning Outcomes
- Understanding the DP Equation and the minimum principle.
- Understanding stochastic control problems in discrete time.
- Understanding Controlled diffusion processes, Dynamic programming principl, Hamilton-Jacobi-Bellman equation, and Verification theorem.
Course Contents
- Deterministic Systems in Discrete-Time
- Stochastic Control Systems in Discrete-Time
- The classical Partial Differential Equation (PDE) approach to dynamic programming
Bibliography
Recommended Core Bibliography
- Continuous-time stochastic control and optimization with financial applications, Pham, H., 2009
Recommended Additional Bibliography
- Financial modeling : a backward stochastic differential equations perspective, Crepey, S., 2013
- Modeling with Ito stochastic differential equations, Allen, E., 2007
- Numerical solution of stochastic differential equations with jumps in finance, Platen, E., 2010
- Stochastic control and mathematical modeling : applications in economics, Morimoto, H., 2010
- Stochastic control in discrete and continuous time, Seierstad, A., 2009