Foreign students graduate courses

Maria Elena De Giuli (1st part)

Mario Maggi (2nd part)
E-mail

degiuli@eco.unipv.it

magma@eco.unipv.it
Educational aim:

The main objective of this course is to present selected topics on quantitative approaches to Economics, Finance and Business.

Quantitative background. Calculus and Optimisation, Linear Algebra: a selected review.

Expected utility and the simple inter-temporal consumption problem.

Asset pricing: Arbitrage, state prices and risk-neutral probabilities.

Asset pricing models: a selected review.

Risk management: Different types of risk, risk measures and hedging. Credit risk and default probabilities.

Numerical methods for optimisation, asset allocation and evaluation. Introduction to Matlab and Scilab languages and programming.
Reading list:

P. Brandimarte, Numerical methods in finance: a MATLAB-based introduction, John Wiley & Sons, New York, 2001.

R.A. Jarrow, V. Maksimovic, W.T. Ziemba, Finance, Handbooks in Operations Research and Management Science, Vol. 9, North Holland, 1995. Chapters: 1, 2, 4, 5, 19.

A.J. McNeil, R. Frey, P. Embrechts, Quantitative Risk Management: Concepts, Techniques, and Tools, Princeton University Press, Princeton, 2005.

C. P Simon, L.E. Blume, Mathematics for Economists, W. W. Norton & Co Inc, 1994.
Assessment:

Written exam and programming exercises.

Elisa Caprari

The course introduces the most important instruments needed to analyze and study the behaviour and properties of solutions of a dynamical system. The problem of Dynamical Optimization is then introduced both in the continuous and the discrete case, and necessary and sufficient optimality conditions are given. Finally, some economical applications of such instruments are presented.

The contents of this course are fundamental for many economical models.
Course program:

1. 
   Dynamical systems. Differential equations and finite differences equations. Systems of differential equations and finite differences equations. Equilibrium solutions for dynamical systems and stability of solutions.The linear case: solutions and stability of equilibrium solutions. Nonlinear case: linearization and Liapunov method.
   
2. 
   Dynamic optimization. Calculus of variation and Eulero’s equation. Transversality conditions. Sufficient optimality conditions. Optimal control and Maximum Principle. Transversality conditions. The case with infinite horizont. Autonomous problems. Economical applications.
   
3. 
   Dynamic programming. Dynamic optimization and Bellman’s principle. Economical applications.
   

Simon C.P. and Blume L.E., Mathematics for Economists, W.W. Norton and Company;

A.C. Chiang, Methods of Mathematical Economics, Mc Graw Hill, Singapore;

Chiang, Elements of Dynamic optimization, Mc Graw Hill, Singapore, 2002;

Leonard D. and Van Long N., Optimal Control Theory and Static Optimization in Economics, CUP Cambrige, 1992;

Intrilligator M.D., Mathematical Optimization and Economic Theory, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971;

De La Fuente A., Mathematical Methods and Models for Economists, Cambridge University Press;

M.I. Kamien, N,L. Schwartz, Dynamic Optimization, The calculus of variations and optimal Control in Economics and Management, North-Holland;

N.L. Stokey, R.E. Lucas Jr., Recursive Methods in Economic Dynamics, Harvard University Press.
Assessment:

Written exam.