Learning objectives
Mod. 1:
- To learn numerical methods for solving financial problems of differential character
- To acquire competence in the analysis of numerical results
Mod. 2:
To provide to the students some specific tools in order to properly investigate current research topics in the frame of kinetic equations for socio-economic sciences.
Course unit content
Mod. 1: Numerical methods for differential problems linked to the Black-Scholes equations for the evaluation of financial options.
Mod. 2:
Introduction to kinetic equations for a simple market economy.
Investigation (from a modelling and an analytical point of view) of several interaction models for wealth exchange:
- basic deterministic model;
- model with random variables;
- model with taxation and redistribution.
Bibliography
Mod. 1:
La maggior parte del programma è basato su:
- P.Wilmott, J. Dewynne and S. Howison, 'Option Pricing', Oxford Financial Press, 1993
- R. Seydel, 'Tools for Computational Finance', Springer, 2009
Mod. 2:
Books or extended reviews:
- B. During, D. Matthes, G. Toscani, "A Boltzmann-type approach to the formation of wealth distribution curves", Riv. Mat. Univ. Parma 1 (2009) 199–261.
- L. Pareschi, G. Toscani, "Interacting multiagent systems. Kinetic equations and Monte Carlo methods", Oxford University Press (2013).
Research papers:
- A. Chakraborti, B.K. Chakrabarti, "Statistical mechanics of money: how saving propensity affects its distributions", Eur. Phys. J. B. 17 (2000), 167-170.
- S. Cordier, L. Pareschi, G. Toscani, "On a kinetic model for a simple market economy", J. Stat. Phys 120 (2005) 253–277.
- D. Matthes, G. Toscani, "On steady distributions of kinetic models of conservative economies", J. Stat. Phys. 130 (2008), 1087-1117.
- M. Bisi, G. Spiga, G. Toscani, "Kinetic models of conservative economies with wealth redistribution", Comm. Math. Sci. 7 (2009) 901–916.
Assessment methods and criteria
Oral exam with any term paper.
