- Oggetto:
ADVANCED STOCHASTIC CALCULUS WITH APPLICATIONS
- Oggetto:
ADVANCED STOCHASTIC CALCULUS WITH APPLICATIONS
- Oggetto:
Academic year 2024/2025
- Course ID
- SEM0229
- Teachers
- Tiziano De Angelis (Lecturer)
Luca Regis (Lecturer) - Degree course
- Generic
- Year
- 2nd year
- Teaching period
- Second semester
- Type
- Elective
- Credits/Recognition
- 6
- Course disciplinary sector (SSD)
- SECS-S/06 - mathematical methods of economy, finance and actuarial sciences
- Delivery
- Formal authority
- Language
- English
- Attendance
- Optional
- Type of examination
- Written
- Prerequisites
- Knowledge of measure theoretic foundations of probability, Brownian motion, stochastic differential equations and Ito formula.
- Oggetto:
Sommario del corso
- Oggetto:
Course objectives
This course illustrates advanced methods and techniques from stochastic calculus which are needed to solve various stochastic control problems. Applications of stochastic control are presented in selected examples from economics, finance and insurance.- Oggetto:
Results of learning outcomes
At the end of the course students will have developed an understanding of stochastic control and its applications in economics, finance and insurance. Students will be capable of:- Formulating a stochastic control problem
- Deriving the associated Hamilton-Jacobi-Bellman equation
- Obtaining a verification theorem with a candidate optimal control
- Oggetto:
Program
- Stochastic differential equations
- Feynman-Kac formula
- Introduction to optimal stopping
- Introduction to stochastic control
- Applications of optimal stopping to American option pricing
- Applications of stochastic control to portfolio optimisation problems and insurance risk management
- Oggetto:
Course delivery
The course is articulated in 48 hours of formal in-class lecture time and in at least as many hours of at-home work solving practical exercises.
- Oggetto:
Learning assessment methods
The course grade is determined solely on the basis of a written test. The test evaluates the student's ability to do the following:
- Present briefly the main ideas, concepts and results developed in the course, also explaining intuitively the meaning and scope of the definitions and the arguments behind the validity of the results
- Use effectively the concepts and the results to answer questions around stochastic calculus, optimal stopping and stochastic control.
The above is accomplished by asking the student to answer open questions (2-4 questions). Questions can be essay questions or exercises. The minimum exam grade is 18/30, the maximum grade is 30/30 cum laude. More details on the exam can be found on Moodle.
The exam is an open-book exam lasting 2 hours. Use of calculators is permitted.
Suggested readings and bibliography
- Oggetto:
- Book
- Title:
- Stochastic calculus
- Year of publication:
- 2017
- Publisher:
- Springer
- Author:
- Paolo Baldi
- ISBN
- Required:
- Yes
- Oggetto:
- Book
- Title:
- Continuous-time stochastic control and optimization with financial applications
- Year of publication:
- 2009
- Publisher:
- Springer
- Author:
- Huyen Pham
- ISBN
- Required:
- Yes
- Oggetto:
- Book
- Title:
- Optimal stopping and free boundary problems
- Year of publication:
- 2006
- Publisher:
- Springer
- Author:
- Goran Peskir and Albert Shiryaev
- ISBN
- Required:
- Yes
- Oggetto:
- Book
- Title:
- Arbitrage theory in continuous time
- Year of publication:
- 2009
- Publisher:
- Oxford University Press
- Author:
- Tomas Bjork
- ISBN
- Required:
- Yes
- Oggetto:
Courses that borrow this teaching
- APPLIED STOCHASTIC CALCULUSLaurea Magistrale (M.Sc.) in Stochastics and Data Science
- APPLIED STOCHASTIC CALCULUS
- Oggetto: