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CIMPA-UNESCO-JORDAN School

Mathematical Modeling for financial Markets

Objectives :

The main objectives of the school are:

1.  Providing an introduction to some topics in financial mathematics for non specialist researchers and postgraduate students. On the other hand, it presents the recent advances in these topics for more specialized researchers.

2.  The organization of this school fits within the framework of the regional research network (Lebanon, Syria, Jordan, Palestine, Iran, Kuwait, Morocco, Tunisia, and Algeria).  This network gathers researchers in the region working in the field of Analyses:  PDE’s, Dynamical Systems, Evolution Equations, and Global Analysis. This school is the third in a series of summer schools in the region.

3.  This school lies within the scope of Euro - Mediterranean Master in Mathematics and Applications.  One of the main topics of this Master will be financial mathematics. 

4.  To promote the exchanges between regional and European mathematicians. 

5. Particular attention will be given to postgraduate students in the region. From one side, to increases their knowledge in the proposed topics and on the other side, they meet researchers in the field. 

Scientific committee:

M. Jazar (Université Libanaise, Lebanon), M. Jeanblanc (Evry, France), Y. Ouknine (Université Cadi Ayyad - Morocco), N. Touzi (ENSAE).

Organizing committee:

M. Alrefaei (Jordan University of Science and Technology), M. Al-Towaiq (JUST), A. Al-Salmann (Yarmouk University), A. El Soufi (Tours), M. Jazar (université libanaise), N. Touzi (ENSAE).

Lecturers:

-        B. Bouchard, Paris 6 (France)

-        S. Crépey, Université d'Evry (France)

-        F. Hamel, Marseille (France)

-        M. Jeanblanc, Evry (France)

-        P. Priaullet, HSBC-CCF (France)

-        R. Monneau, école nationale des ponts et chaussées (France)

-        Y. Ouknine, université Cadi Ayyad (Morocco)

-        N. Touzi, ENSAE

Working languages:

French, English

Date and location :

September 11-22, 2005, Irbid (Jordan)

Scientific programme:

1 - Partial differential equations and process of diffusion:  F Hamel

­        Recall on the parabolic PDE’s and the SDE’s

­        Feynman-Kac Formula

­        Probability of change and cash;  theorem of Girsanov

2 - Pocket money optimization:  Y. Ouknine

­        Stochastic control;  result of Markowitz

­        Pocket money insurance

3 - Numerical Methods for the option pricing: B. Bouchard

­        Binomial and trinomial trees

­        Monte Carlo

­        Finite differences method

­        High dimensional problem

4 - Financial Instruments; cover in imperfect market:  N. Touzi and P. Priaullet

­        Characteristics of the contracts

­        Examples on markets actions, changes, rates

­        Relations of arbitration

­        Criterion of average variance

­        Utility function

­        Indifference prices;  non-linear pricing

5 - Products with optimal exercise and free boundary problems:  R. Monneau

­        Bermuda Options

­        American options

7 - Calibration of models: S. Crépey

­        Modeling of stochastic volatility

­        Calibration by Tychonov regularization

8 - Models of the curve rates:  M. Jeanblanc

­        Short rates models:  Vasicek, Hull-White

­        Heath-Jarrow-Morton models

­        Market models:  Approach of Brace-Gatarek-Musiela

Prerequisites :

Researchers and postgraduate students

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Last update : 2006-01-13.