Courses taught:
1. MACROECONOMICS (331-2202) [-C-] :
Semester B Course
(3hours Theory and 2 hours Lab/Tutorial Exercises)
5 Teaching Points and 6 ECTS Points
2. FINANCIAL MATHEMATICS II (331-3402) [-E2-]
Semester F Course
(3 hours Theory and 2 hours Lab/Tutorial Exercises)
5 Teaching Points and 6 ECTS Points
Course Contents:
The course refers to the finite time-horizon and state-space Financial Mathematics.
1) Uncertainty and information- Unfolding of information and information partitions of the state space- Event-tree and stochastic exchange economies- Stochastic exchange economy commodity space- Financial contracts in stochastic economies and sorts of them- Vectors of prices and payoff vectors of financial contracts, financial markets in the event-tree model- Positions of investors towards the financial contracts- Portfolios, payoff matrix and payoff subspace of a financial market- Self-financing portfolios, complete and incomplete markets, contingent claims and hedging portfolios for contingent claims, hedging portfolios and completeness of a market- Completion of a market with options and the theorem of Ross- Budget sets in stochastic exchange economies- The investor’s optimization problem in stochastic exchange economies- Arbitrage and its relation with the investor’s optimization problem- Characterization of the absence of arbitrage in financial markets and arbitrage pricing of financial contracts- Relation between completeness of the market and arbitrage pricing-Derivatives of European type and their relation to the general form of contingent claims in the event-tree model.
2) Algebras of sets and partitions in finite probability spaces- Conditional expectation and finite-time martingale process in finite probability spaces- Filtrations and event-trees- Stochastic processes being adapted on an event-tee- Equivalent martingale measures of probability and absence of arbitrage in the event-tree model of financial markets –Completeness of a market and equivalent martingale measures.
Prerequisite(s):
Applied Linear Algebra I
Applied Linear Algebra II
Calculus I
Calculus III
Probabilities II
Learning outcomes:
Students who have successfully completed the course will have:
1. been familiar with the essential notions of Financial Mathematics at a first level of generality.
2. understood the relationship between the martingale stochastic processes and no-arbitrage pricing of contingent claims.
3. received the required background in order to attend more advanced courses on Financial Mathematics
Follow-up Courses: Financial Mathematics III
Textbooks used:
1) Ì. Magill, M. Quinzii, ‘Theory of Incomplete Markets : Volume I’, MIT Press (1996)
2) S. LeRoy , J. Werner, ‘Introduction to Financial Economics’, Cambridge University Press (2001)
3. DERIVATIVES
[-E-postgraduate]Semester B Course
(2 hours Theory)
2 Teaching Points
4. RISK MANAGEMENT [-E-postgraduate]
Semester B Course
(2 hours Theory)
2 Teaching Points
Course Contents:
Financial positions if the set of the states of the world is finite- Financial risk- Acceptance sets and their geometry (wedges and cones)- Coherent risk measures –The risk measure being associated with an acceptance set- The values of a risk measure as risk premia for the financial positions- The continuity of coherent risk measures – The risk measure being associated with a set of scenarios for the states of the world- The representation theorem of coherent risk measures and its interpretation. Generalization of Markowitz portfolio selection model using coherent risk measures.
Prerequisite(s):
Calculus I
Calculus III
Real Analysis
(in the way that most of greek universities’ students of mathematical direction have been taught)
Learning outcomes:
Students who have successfully completed the course will have:
1) been familiar with the mathematical aspects of the coherent and convex risk measures’ theory, which was developed during the past ten years as an attempt of finding new methods for measuring financial risk that overcome the disadvantages of older such methods, just like of the ones implied by the method of Value at Risk.
Follow-up Courses:
Textbooks used:
(for the second part of the course)
1. P. Artzner, F. Delbaen, J.M. Eber, D. Heath, ‘Coherent measures of risk’, Mathematical Finance 9, 203-228.
2. H. Föllmer, A. Schied, "Convex measures of risk and trading constraints", Finance and Stochastics 6 (2002), 429-447.
3. "Risk measures in finite spaces", introductory notes of Ch. Kountzaki.
4. RISK MEASURES IN FINITE SPACES, notes of Ch. Kountzaki.
5. Microeconomics
6. Introduction to Financial Mathematics
7. Applied Analysis
8. Portofolio Optimazation
9. Reinsurance
10. Mathematical Economics
11. Financial Modelling (Postgraduate course)
12. Calculus II
Courses of winter semester 2011-2012