6 EC
Semester 1, period 1, 2
5374POTS6Y
| Owner | Master Mathematics |
| Coordinator | dr. A.J. van Es |
| Part of | Master Mathematics, year 1Master Stochastics and Financial Mathematics, year 1 |
In this course we treat fundamental economic notions as preference relations and utility functions and show how these are applied in portfolio optimization and measure of risk. This will be done first for static markets and extended later on to a dynamic setting, where time is discrete. Finally we will consider finding hedging and super hedging strategies.
Lecture notes: Portfolio Theory, Peter Spreij, november 2014
The student should:
- be able to explain the theory of the course as outlined below
- be able to apply the theory to solve exercises
Lectures and exercises.
|
Activity |
Number of hours |
| Lectures |
28 |
| Self study |
28 |
|
Exercises |
42 |
The programme does not have requirements concerning attendance (OER-B).
| Item and weight | Details | Remarks |
|
Final grade | ||
|
25% Exercises | ||
|
75% Final oral exam | Allows retake |
The grade for the exercises is the average of the weekly grades.
During the oral exam we review the content of the course globally. The student is aked to study his choice of five theorems with their proofs in detail. About three of those will be examined
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.uva.nl/plagiarism
| Weeknummer | Onderwerpen | Studiestof |
| 1 | Market, portfolio, arbitrage, risk neutral measures, Fundamental Theorem of Asset Pricing | Chapter 1. Section 1.1 |
| 2 | Principle of one price, contingent claims and derivatives, arbitrage free price of a contingent claim. We skipped the proof of Theorem 1.15. | Chapter 1. Section 1.2 up to Theorem 1.15 |
| 3 | Set of arbitrage free prices for a contingent claim. Complete markets | Chapter 1. Finish Section 1.2 and Section 1.3. |
| 4 | Preferences, preference relations, numerical representation.. | Chapter 2 up to Definition 2.8 |
| 5 | Preference relations continued. We skipped the proof Proposition 2.10. | Chapter 2 |
| 6 | Lotteries. Von Neumann-Morgenstern representation. Independence and Archimedean axioms. | Chapter 3. Section 3.1 |
| 7 | Lotteries continued. Utility and expected utility. Risk aversion. | Chapters 3. Section 4.1 |
| 8 | Free | |
| 9 | Arrow Pratt coefficient of risk aversion. Chapter 6, optimization and absence of arbitrage, up to the proof of Theorem 6.5. | Chapter 4. Skip Chapter 5, Proceed with Chapter 6 |
| 10 | Proof of Theorem 6.5. | Chapter 6 |
| 11 |
Finish Section 6.1. Skip Section 6.2. Chapter 7, optimal contingent claims, up to Theorem 7.2 and its proof. We skipped the rest of the chapter. Chapter 8, update of definitions to the dynamic (more time points) setting, up to proposition 8.7 (proof next week). |
Chapter 6. Chapter 7 |
| 12 | Dynamic arbitrage theory. Self-financing trading strategies and arbitrage. Fundamental Theorem of Asset Pricing in discrete time. | Chapter 8 |
| 13 | European contingent claims. Complete markets. | Chapter 8 |
| 14 | Optimization in dynamic models. Dynamic programming. | Chapter 9. Sections 9.1 sn 9.2. |
| 15 | Consumption investment and martingale method. | Chapter 9. Section 9.3. |
| 16 |
The schedule for this course is published on DataNose.
Recommended prior knowledge: Measure Theoretic Probability.