Portfolio Theory

6 EC

Semester 1, period 1, 2

5374POTS6Y

Owner Master Mathematics
Coordinator prof. dr. P.J.C. Spreij
Part of Master Mathematics, Master Stochastics and Financial Mathematics, Master Mathematics, specialization Algebra and Geometry, year 1Master Mathematics, specialization Analysis and Dynamical Systems, year 1Master Mathematics, specialization Mathematical Physics, year 1Master Mathematics, specialization Stochastics , year 1Master Stochastics and Financial Mathematics, specialization Data Analysis and Statistics, year 1Master Stochastics and Financial Mathematics, specialization Financial Mathematics, year 1Master Stochastics and Financial Mathematics, specialisation Probability and Decision Making, year 1Master Mathematics, specialisation Discrete Mathematics and Quantum Information, year 1

Course manual 2022/2023

Course content

In this course we treat the foundations of mathematical finance, its fundamental concepts like arbitrage, equivalent martingale measures, and fundamental economic notions as preference relations and utility functions and show how these are applied in portfolio optimization. This will be done first for static markets and extended later on to a dynamic setting, where time is discrete. Finally we will show how stochastic control theory and dynamic programming can be applied to problems of portfolio optimization.

Study materials

Literature

Syllabus

Objectives

  • The general aim is to make students familiar with the mathematical foundations of mathematical finance in discrete time and the fundamentals of portfolio selection. In particular, students will able to prove a number of well selected theorems and demonstrate in assignments that they master the theory. Specific objectives to be met at the end of the course follow.
  • Students are familiar with fundamental concepts of financial mathematics (arbitrage and completeness) and know how to apply them.
  • Students know the theory behind portfolio optimization and know how to solve such optimisation problems.
  • Students are able to optimize under order restrictions.
  • Students know results about dynamic arbitrage theory and completeness in multi-period (discrete time) models.
  • Students know how to apply dynamic programming to investment-consumption problems.

Teaching methods

  • Lecture
  • Excercises

Lectures and exercises.

Learning activities

Activity

Number of hours
Lectures

28
Self study

66

Exercises

66

 

Attendance

This programme does not have requirements concerning attendance (TER-B).

Assessment

Item and weight Details

Final grade

The grade for the exercises is the average of the weekly grades, this grade counts for 40% of the final grade. The other 60% is the grade for the oral exam. The weekly assignments have to be made in pairs, this is mandatory!

During the oral exam we review the content of the course globally. The student is aked to study his/her choice of four theorems with their proofs in detail. If one fails the first attempt then we reschedule for a resit. The exercises also contribute to the final grade after the resit.

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Weeknummer Onderwerpen Studiestof
1 see homepage or Canvas  
2    
3    
4    
5    
6    
7    
8    
9    
10    
11    
12    
13    
14 Extra session if needed.  
     
     

Timetable

The schedule for this course is published on DataNose.

Additional information

Recommended prior knowledge: Measure Theoretic Probability.

Contact information

Coordinator

  • prof. dr. P.J.C. Spreij

 

Staff

  • R.T. Kamphuis