CAMEF (2007-8) :: Pretoria workshop - programme

Last modification : 2007/11/22 09:48

This website is also available at http://www.bittyurl.com/?3af124 .

Any interested person is welcome to attend these lectures. However, we request that you notify the organisers in advance of your attention to do so - especially for the Tuesday afternoon and the Thursday sessions. Staff and students of Unisa - especially the Department of Decision Sciences - will be particularly welcome.

Participants: please confirm for lunch on Tuesday and the conference dinner for Wednesday - these have to be booked. There is a limit of 20 people for Tuesday's lunch but there are still a few places available.


The programme is now semi-final but please check this page again by Monday 2007-11-19 as a small number of last-minute changes are - of course - possible.

Monday, 19/11


12:00-14:00 Practical arrangements at Unisa for Hungarian participants, who arrive in the morning.
14:00-16:00 Planning - Budapest workshop

Tuesday, 20/11


Venue: Unisa Senate Hall (morning, near main entrance in the Theo van Wijk Building, see campus map http://www.unisa.ac.za/default.asp?Cmd=ViewContent&ContentID=6954) & Voortrekker Monument restaurant (afternoon, booked through Mr Pierre van Zyl, 012 321 6230 and paid by electronic transfer 2007-11-15)
Technology: data projector, overhead projector (for paper or transparencies)

09:30-10:30 Fouché, Willem: Recent developments in the interaction between mathematical logic and dynamical systems
10:30-11:00 Gumbo Victor & Swart, Barbara: The SAFEX-JIBAR model
11:00-11:30 Coffee Break (refreshments not provided - Unisa's Philadelphia cafeteria is just upstairs)
11:30-12:30 Mala, József : Path independent choice functions
13:00-14:00 Lunch at Voortrekker Monument http://www.voortrekkermon.org.za/ (RSVP, at Voortrekker Monument Restaurant - mention "UNISA function" when enterering complex as you would otherwise need to pay the entrance fee)
> Confirmed for lunch: Swart, Potgieter, Tallos, Medvegyev, Mala, Pintér, Kánnai, Magyarkúti, Birch, Geist, Makananise, Venter, Davie, Rosinger, Swanepoel, Fouché, Gumbo (non-vegetarian), Brattka (vegetarian).
14:00-16:00 Seminar: Ontology and epistemology of probability in economics and finance (RSVP, at Voortrekker Monument Restaurant)
> 14:00-14:30 Davie, George: Gambling against a random sequence
> 14:30-15:00 Brattka, Vasco: Randomness with respect to the Signed-Digit Representation
> 15:00-16:00 Panel discussion
16:00-17:00 At leisure - Voortrekker Monument

Wednesday, 21/11


Venue: Unisa, TvW 10-150 (Theo van Wijk Building, see http://www.unisa.ac.za/default.asp?Cmd=ViewContent&ContentID=13999)
Technology: data projector, white or black (to be confirmed) board

09:30-10:30 Medvegyev, Péter: No-arbitrage theorems in mathematical finance, Part I
10:30-11:00 Coffee Break (refreshments not provided)
11:00-12:00 Pintér, M. : The non-existence of complete, universal topological type space
12:00-12:30 Potgieter, Petrus: Elementary topology and computability
12:30-13:30 Break for lunch
13:30-14:30 Kánnai, Zoltán and Tallos, Peter: Viability theory and economic modeling
14:30-15:00 Ntwiga, Davis: TBA
15:00-17:00 Unstructured excursion (depending on the weather) to Pretoria's city centre, possibly including places of worship or the Zoo.

19:00-22:00 Workshop dinner (venue: BOER'geoisie http://www.dining-out.co.za/member_details.asp?MemberID=2506 Greenlyn Village, 13th Street, Menlo Park, 012 460 0264)

Thursday, 22/11


Venue: The Innovation Hub, Boardrooms 2 & 3 (all day, http://www.theinnovationhub.com/ - booking made through Ms Johanna Tilodi and paid by electronic transfer 2007-11-15)
Technology: data projector (dual screens), large white board, Internet available in venue

09:30-10:30 Magyarkúti, Gyula: Hara's elementary proof of Afriat's theorem
10:30-10:45 Coffee break (provided in venue)
10:45-11:45 Potgieter, Paul: The fractal geometry of Brownian motion
11:45-12:45 Brattka, Vasco: Tutorial on Computable Analysis, Part I
12:45-13:15 Potgieter, Petrus: On the computability of the Brouwer fixed-point theorem
13:15-14:00 Break for lunch (restaurant available, for participants' own account)
14:00-14:30 Invitation to Python (Moritz Braun)
14:30-16:30 Seminar: LaTeX tips and tricks - open source typesetting of mathematics
> A variety of 10 minute sessions:
>> To use numprint or not? (Petrus Potgieter)
>> The process of creating TeX documents (Gyula Maguarkúti)
>> Venda diacritics in LaTeX (Mashudu Makananise)
>> Beamer is for strippers (Petrus Potgieter)
>> Font issues in LaTeX (Chris Swanepoel)
>> LaTeX and multilingual content (Petrus Potgieter)
16:30-18:00 Optional visit to Pretoria Botanical Gardens http://www.sanbi.org/frames/pretoriafram.htm (entrance fee: R15,00)

Friday, 23/11


Venue: AJH 4-116, Unisa main campus : AJH van der Walt Building - Decision Sciences seminar room.

09:30-10:30 Kánnai, Zoltán: Farkas' theorem and smooth programming easily
10:30-10:45 Coffee break
10:45-11:45 Medvegyev, Péter: No-arbitrage theorems in mathematical finance, Part II


Talk abstracts


Participants should post their talk titles and abstracts here. Use the wiki syntax as in the example. The name of the speaker and the title of the talk are final when entered here. Feel free to come back and edit your abstract. Please put the presenter's name first in the case of contributions with more than one author and keep alphabetical order by the surname of the presenter.


Brattka, Vasco & Archibald, Margaret & Heuberger, Clemens: Randomness with respect to the Signed-Digit Representation

The ordinary notion of algorithmic randomness of reals can be characterised as Martin-Löf randomness with respect to the Lebesgue measure or as Kolmogorov randomness with respect to the binary representation. In this paper we study the question how the notion of algorithmic randomness induced by the signed-digit representation of the real numbers is related to the ordinary notion of algorithmic randomness. We first consider the image measure on real numbers induced by the signed-digit representation. We call this measure the signed-digit measure and using the Fourier transform of this measure and the Riemann-Lebesgue Lemma we prove that this measure is not absolutely continuous with respect to the Lebesgue measure. We also show that the signed-digit measure can be obtained as a weakly convergent convolution of discrete measures and therefore, by a classical Theorem of Jessen and Wintner the Lebesgue measure is not absolutely continuous with respect to the signed-digit measure. Finally, we provide an invariance theorem which shows that if a computable map preserves Martin-Loef randomness, then its induced image measure has to be absolutely continuous with respect to the target space measure. This theorem can be considered as a loose analog for randomness of the Banach-Mazur theorem for computability. Using this Invariance Theorem we conclude that the notion of randomness induced by the signed-digit representation is incomparable with the ordinary notion of randomness.

Davie, George: Gambling against a random sequence

Length: 30 minutes.

Fouché, Willem: Recent developments in the interaction between mathematical logic and dynamical systems

We discuss how one can use the dynamical properties of Brownian motion to establish results in descriptive set theory. We also discuss some results of Mathias that depict how answers to some basic problems in symbolic dynamics are independent of the axioms of set theory. Length: 60 minutes.

Gumbo Victor & Swart, Barbara: The SAFEX-JIBAR model

The LIBOR market model is at the centre of active research the world over. Various approaches are being suggested mainly based on the market-accepted Black's formula for caps and floors. We present a model that is commensurate with the South African market, the SAFEX-JIBAR model, based on the assumption that the forward JIBAR rates follow a log-normal process. The corresponding Greeks are easily deduced.

Kánnai, Zoltán : Farkas' theorem and smooth programming easily

The following statement for linear inequalities has fundamental importance in mathematical programming:
Theorem 1 (Farkas' lemma) For given vectors a, a1 , . . . , am ∈ Rn , if the inequality a, x ≤ 0 is a consequence of the system of inequalities a1 , x ≤ 0, . . . , am , x ≤ 0, then a is a nonnegative combination of a1 , . . . , am .
This theorem is generally known as a relatively hard statement.The simplification of its proof has mainly educational importance. The original proof of Farkas,and also further works are quite elementary, but not suggestive at all; other papers are more elegant but use hard techniques of Euclidean or even Hilbert spaces. Recently, Broyden, and Komornik gave simpler proofs, but both of them still capitalize the Euclidean metric property. Here we present Farkas' lemma as one of the introductory statements of linear algebra, suitable to be discussed even at the beginning of the education. The only key to the simplification (and to some generalization) is the specific language of the abstract linear algebra. It makes also possible to easily discuss problems of smooth programming at a quite early period of the education, without hard devices of functional analysis.
Length: 60 minutes.

Mala, József : Path independent choice functions

Path independent choice functions were investigated first by Plott (1973) but the theory of such functions began to develop only in 1999 after the discovery of Koshevoy who found that path independent choice functions were closely connected to the theory of abstract convex geometries. The theory of path independent choice functions can give a way out of Arrow's impossibility theorem, since transitivity seems too strong a requirement for the society and path independent choice functions are regarded as the ultimate tools representing rationality. Length: 60 minutes.

Magyarkúti, Gyula: Hara's elementary proof of Afriat's theorem

A finite set of pairs of prices and demands are rationalizable if there exists monotone, concave, locally nonsatiated utility function such that the demands are maximizers of the utility function above the budget set determined by the price belonging to the demand. The Afriat's theorem (1967) gives a necessary and sufficient assumption for the observed price-demand pairs to be rationalizable. Based on Chiaki Hara's unpublished paper we discuss an elementary proof, and clarify the relationship with the Spilrajn type extension theorems. Length: 60 minutes.

Medvegyev, Péter: No-arbitrage theorems in mathematical finance

Length: 2x60 minutes

Pintér, M. : The non-existence of complete, universal topological type space

In the literature of complete, universal topological type space, a meta topological assumption is imposed on the topology used as the structure of the beliefs. In order to build complete, universal type space all previous works have assumed two additional topological assumptions, the Hausdorff property of the topological spaces involved in the analysis and the compact regularity of the probability measures used for modeling the beliefs of the players. In this talk we give an introduction into the theories of hierarchies of beliefs, games with incomplete information, Harsányi type space, and show that the two above mentioned ``endogenous'' assumptions can be weaken, moreover we give an example which implies that there is no complete, universal topological type space in the category of topological type spaces meet the meta topological, and the retained inherent topological (quasi-compact, closed regularity) assumptions. Length: 60 minutes.

Potgieter, Paul: The fractal geometry of Brownian motion

Length: 60 minutes.

Potgieter, Petrus H. : On the computability of the Brouwer fixed-point theorem

The Orevkov counter-example in detail. Length: 30 minutes.

Potgieter, Petrus H. : Elementary topology and computability

The talk illustrates, in a completely elementary way, how topological considerations can determine limits for a general theory of computability on a topological space. It proceeds from the assumption that any reasonable notion of computability implies that all computable functions are continuous. Length: 30 minutes.

Kánnai, Zoltán and Tallos, Peter: Viability theory and economic modeling

A brief introduction into the theory of differential inclusions, viability theory and selections of set valued mappings is presented. As an application the implicit scheme of the Leontief dynamic input-output model is considered. Length: 60 minutes.