PhD School in. Economics, Applied Mathematics and Operational Research
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1 October 2012 PhD School in Economics, Applied Mathematics and Operational Research Classes timetable (with bibliography) and test to be attended during the first year - cycle XXVIII Prof. Valeria Caviezel, Via dei Caniana 2, Bergamo Tuesday 2 October 10,00-13,00 Room 23 Thursday 4 October 10,00-13,00 Room 16 Tuesday 9 October 10,00-13,00 Room 23 Thursday 11 October 10,00-13,00 Room 23 Wednesday 17 October 10,00-13,00 Room 18 Thursday 18 October 10,00-13,00 Room 16 Tuesday 23 October 10,00-13,00 Room 23 Thursday 25 October 10,00-13,00 Room 18 Tuesday 30 October 10,00-13,00 Room 23 Tuesday 6 November 10,00-13,00 Room 13 Thursday 15 November 10,00-13,00 Room 2 Tuesday 27 November 10,00-13,00 Room 17 Probability and financial stàtistics Bibliography: Knowledge of basic STATISTICS and PROBABILITY are required. It is important to know the topics covered in the following books: 1. S. Borra & A. Di Ciaccio, Statistica Metodologie per le scienze economiche e sociali, McGraw-Hill. or 2. G. Cicchitelli, Probabilità e statistica - II edizione, Maggioli editore (no ch. 9, 11). or 3. S.M. Ross, Introductory statistics 2 nd edition, Elsevier Academic Press (no ch. 11, 14, 15). (There is a translation in Italian). During the first PhD year the concepts of statistics and probability will go into more depth: 1. G. Casella & R.L. Berger, Statistical Inference, Duxbury Advenced Series. or 2. A.M. Mood, F.A. Graybill & D.C. Boes, Introduction to the theory of statistics, Mc Graw-Hill. (There is a translation in Italian). or
2 R.V. Hogg & A.T. Craig, Introduction to mathematical statistics 6 th edition, Mc Millan. FINAL EXAMINATION: 21 November ,00-13,00 Room 23 Dott Annamaria Bianchi, Via dei Caniana 2, Bergamo Thursday 25 October 14,00-17,00 Room 18 Friday 26 October 10,00-12,00 Room 23 Monday 29 October 10,00-13,00 Room 23 Wednesday 31 October 10,00-13,00 Room 22 Monday 5 November 10,00-13,00 Room 22 Wednesday 7 November 10,00-13,00 Room 22 Friday 9 November 10,00-13,00 Room 22 Thursday 22 November 10,00-13,00 Room 23 Measure theory Bibliography: Real Analysis, Modern Techniques and their applications. author: Gerald B. Folland Wiley-Interscience FINAL EXAMINATION: 20 December ,00-18,00 Room 18 November 2012 Prof. Emilio Spedicato, Via dei Caniana 2, Bergamo Monday 5 November 15,00-17,00 Room 22 Thursday 8 November 15,00-17,00 Room 23 Monday 12 November 15,00-17,00 Room 22 Tuesday 13 November 15,00-17,00 Room 23 Wednesday 14 November 14,00-16,00 Room 22 Thursday 15 November 15,00-17,00 Room 23 Monday 19 November 15,00-17,00 Room 23 Tuesday 27 November 15,00-17,00 Room 23 Thursday 29 November 15,00-17,00 Room 23 Monday 3 December 15,00-17,00 Room 23 Wednesday 5 December 15,00-17,00 Room 22 Thursday 6 December 15,00-17,00 Room 22 Numerical solution of linear systems ABS methods for linear and nonlinear systems FINAL EXAMINATION:
3 dott. Annamaria Bianchi, Via dei Caniana 2, Bergamo Friday 7 December 10,00-13,00 Room 22 Monday 10 December 10,00-13,00 Room 23 Wednesday 12 December 10,00-13,00 Room 22 Tuesday 18 December 10,00-13,00 Room 23 Wednesday 19 December 10,00-13,00 Room 22 Friday 21 December 10,00-13,00 Room 23 Monday 7 January 10,00-13,00 Room 23 Wednesday 9 January 10,00-13,00 Room 23 Friday 11 January 10,00-13,00 Room 23 Stochastic Processes FINAL EXAMINATION: 31 January ,00-18,00 Room 23 January 2013 Prof. Elisabetta Allevi, Università degli Studi di Brescia Sala Riunioni 3 Sede Brixia Via S. Faustino n Brescia Tuesday 15 January 9,30-13,30 Friday 18 January 9,30-13,30 Wednesday 23 January 9,30-13,30 Wednesday 30 January 9,30-13,30 Wednesday 6 February 9,30-13,00 Static optimization Bibliography: Carl P. Simonm, Lawrence Blume, Mathematics for Economist, W.W. Norton Company, Inc Subject propedeutici al corso: Parte I, II, III(Cap. 12,13,14), VI (Cap. 26, 27, 28.1). Program - Calculus (continuous functions, differentiable and continuously differentiable functions, partial derivatives and directional derivatives, gradient, quadratic forms, definite and semidefinite matrices, the intermediate and mean value theorem, Weierstrass theorems, the inverse and implicit function theorems). - Classical optimization: unconstrained and equality constrained problems; - Optimality conditions for constrained extrema; - Convex analysis (separability, convex sets and functions);
4 - Optimality conditions for convex programs; - Generalized convexity (quasiconvex and pseudoconvex functions); - Linear programming ( preliminaries, introduction to duality theory, the duality theorem) The written test at the end of the course will be based on the subjects dealt in the course and on the propaedeutic subjects to the course. FINAL EXAMINATION: February, h. 14,30 Prof. Vito Fragnelli, Università del Piemonte Orientale, Via dei Caniana n. 2, Bergamo Tuesday 22 January 9,30 Room 22 Conference "Communication Structures and Incompatible Agents" Prof. Encarnaҫion Algaba, Università di Siviglia, Via dei Caniana n. 2, Bergamo Tuesday 22 January 9,30 Room 22 Conference "A new approach to the Myerson and position values in Communication Structures" February 2013 prof. Maria Teresa Vespucci, Via dei Caniana 2, Bergamo Tuesday 5 February 9,30-12,30 Room 23 Tuesday 19 February 14,30-17,30 Room 22 Tuesday 26 February 9,30-12,30 Room 23 Tuesday 5 March 9,30-12,30/14,30-15,30 Room 23 Thurdsday 14 March 9,30-12,30 Room 20 Tuesday 19 March 14,30-17,30 Room 23 Wednesday 20 March 14,30-17,30 Room 23 Linear Optimisation FINAL EXAMINATION: May 24, 2013 h. 16,30-19,30 Room 22 Prof. Luca Bertazzi, Università degli Studi di Brescia - Dipartimento di Metodi Quantitativi Contrada S. Chiara, 50 Thurdsday 21 February : Modelli di programmazione lineare intera Thurdsday 28 February : Metodi esatti Thurdsday 7 marzo : Metodi euristici e analisi del caso peggiore
5 Mixed integer linear programming: models and algorithms FINAL EXAMINATION: 17 APRIL 2013 H. 10,00-13,00 Prof. Guido Perboli, Politecnico di Torino, Via dei Caniana n. 2 Bergamo Monday 11 February 15,00 Room 22 Seminar The multi-path Traveling Salesman Problem with stochastic travel costs: models and approximations March 2013 prof. Francesca Maggioni, Via dei Caniana 2, Bergamo Monday 4 March 10,00-13,00 Room 22 Wednesday 6 March 10,00-13,00 Room 22 Friday 8 March 10,00-12,00 Room 23 Monday 11 March 13,30-16,30 Room 17 Wednesday 13 March 10,00-13,00 Room 14 Monday 18 March 13,30-16,30 Room 23 Wednesday 20 March 10,00-13,00 Room 23 Monday 25 March 13,30-16,30 Room 22 Wednesday 27 March 14,00-17,00 Room 18 Tuesday 16 April 14,30-17,30 Room 18 Friday 19 April 10,30-13,00 Room 20 Nonlinear Optimization FINAL EXAMINATION: May, h. 14,00 Room 2 Prof. Maria Grazia Speranza, Università degli Studi di Brescia - Sala Riunioni Dipartimento di Metodi Quantitativi C.da S. Chiara 50 Friday 15 March 9,00-13,00: Modelli e metodi per problemi di scelta di portafoglio Tuesday 19 March 9,00-13,00: Modelli e metodi per problemi di routing Tuesday 26 March 9,00-13,00: Modelli e metodi per problemi di logistica Mixed integer linear programming: models and algorithms FINAL EXAMINATION: 17 APRIL 2013 H. 10,00-13,00 April 2013
6 prof. Gianfranco Gambarelli, Via dei Caniana 2, Bergamo Tuesday 2 April 9,30-12,30 Room 23 Wednesday 3 April 9,30-12,30 Room 23 Thursday 4 April 9,30-12,30 Room 23 Friday 5 April 9,30-12,30 Room 23 Tuesday 9 April 9,30-12,30 Room 23 Wednesday 10 April 9,30-12,30 Room 23 Thursday 11 April 9,30-12,30 Room 23 Monday 22 April 9,30-12,30 Room 22 CANCELLED Wednesday 24 April 16,00-19,00 Room 22 Teoria dei giochi FINAL EXAMINATION: April, h Room 22 Prof. Adriana Gnudi, Via dei Caniana 2, Bergamo Tuesday 2 April 14,00-18,00 Room 23 Wednesday 3 April 14,00-18,00 Room 23 Thursday 4 April 14,00-18,00 Room 23 Tuesday 16 April 9,00-13,00 Room 22 Thursday 18 April 9,00-13,00 Room 18 Wednesday 24 April 9,00-13,00 Room 14 Sistemi dinamici FINAL EXAMINATION: 8 MAY 2013 H. 9,00-13,00 ROOM 14 Prof. Giancarlo Graziola, Via dei Caniana 2, Bergamo Monday 8 April 14,00-17,00 Room 22 Friday 12 April 14,00-17,00 Room 23 Thursday 18 April 14,00-17,00 Room 18 Monday 15 April 14,00-17,00 Room 21 CANCELLED Monday 22 April 14,00-17,00 Room 21 CANCELLED Tuesday 23 April 10,30-12,30 Room 20 PRACTICE EXERCISES Monday 29 April 14,00-17,00 Room 20 Microeconomia Prof. Giovanni Urga, Via dei Caniana 2, Bergamo Wednesday 17 April 14,00-18,00 Room 21
7 Friday 19 April 14,00-18,00 Room 23 Saturday 20 April 8,30-12,30 Room 23 Thursday 9 May 14,00-18,00 Room 22 Friday 10 May 14,00-18,00 Room 14 Saturday 11 May 8,30-12,30 Room 23 Tuesday 21 May 14,00-18,00 Room 23 Wednesday 22 May 14,00-18,00 Room 18 Econometrics FINAL EXAMINATION: 4 June ,30-12,30 Room 22 May 2013 Prof. Giorgio Consigli, Via dei Caniana n. 2, Bergamo Tuesday 14 May 9,30-13,30 Room 23 Wednesday 15 May 9,30-13,30 Room 23 Thursday 16 May 9,30-13,30 Room 23 Friday 17 May 9,30-13,30 Room 22 Stochastic Programming Prof. Steven Fazzari, Professor of Economics, Washington University, St. Louis MO, U.S.A., Via dei Caniana 2, Bergamo Thursday 23 May 10,00-13,00 Room 22 Friday 24 May 10,00-13,00 Room 22 Monday 27 May 10,00-13,00 Room 22 Tuesday 28 May 10,00-13,00 Room 22 Reflections of the State of Macroeconomics Keynesian Growth and Instability The Great Recession as End of the Consumer Age Assessing Fiscal Austerity from a Keynesian Perspective Dott. Janos D. Pinter, DSc Pinter Consulting Services, Inc., Via dei Caniana n. 2 Bergamo Wednesday 29 May 11,00-12,00 Room 22 Seminar Global Optimization in Practice: A Review of Some Recent Applications June 2013
8 Prof. Nagy Tamas, University of Miskolc - Department of Applied Mathematics, Via dei Caniana n. 2, Bergamo Thursday 6 June 10,00-13,00 /14,00-17,00 Room 22 Mixed integer programming Prof. Young Shin (Aaron) Kim, Karlsruhe Institute Technology, Via dei Caniana 2, Bergamo Monday 10 June 10,00-13,00/14,00-17,00 Room 22 Tuesday 11 June 10,00-13,00 /15,00-17,00 Room 22 Wednesday 12 June 10,00-13,00 Room 22 Thursday 13 June 10,00-13,00/15,00-17,00 Room 22 Friday 14 June 10,00-13,00/15,00-17,00 Room 22 Monday 17 June 10,00-13,00 Room 22 Tuesday 18 June 10,00-13,00/15,00-17,00 Room 22 Wednesday 19 June 10,00-13,00 Room 22 Thursday 20 June 10,00-13,00 Room 22 Friday 21 June 10,00-13,00 Room 22 Monday 24 June 10,00-13,00/15,00-17,00 Room 22 Tuesday 25 June 10,00-13,00/15,00-17,00 Room 22 Wednesday 26 June 10,00-13,00/15,00-17,00 Room 22 Thursday 27 June 10,00-13,00/15,00-17,00 Room 22 Friday 28 June 10,00-13,00/15,00-17,00 Room 22 Monday 1 July 10,00-13,00 / 15,00-17,00 Room 22 EXAM 1+2^ PART: Wednesday July 5, 2013 h. 10,00-13,00/15,00-17,00 ROOM 22 PART I. Introduction to Mathematical Finance Primary Asset Valuation: Discrete and Continuous Models (random walks, continuous time limits - diffusions), Forward and backward equations, Frequently Occurring Continuous Stochastic Processes; Arithmetic Brownian Motion; Geometric Brownian Motion; Mean-Reverting Process; Ito's Lemma and Its Multivariate Extensions; Introduction to Jump Processes; Limitations of Diffusions as Models; Simple Financial Applications of Ito's Lemma; Time- Inhomogeneous Cases; Separability and Homogeneity of Cash Flows; Discount Rate for Financial Assets; Recursive Techniques in Asset Valuation. Pricing Derivative Securities: Basic Concepts (Underlying Asset Prices, Futures, Options and Other Derivatives, Interest Rates and Bonds); Black- Scholes Theory (Arbitrage Opportunities, Pricing Forward and Futures Contracts, European Option Pricing, the Black-Scholes PDE, and Risk- Neutrality, Closed Form Solutions, Extensions to Path- Dependent Options);
9 Numerical Methods of Option Pricing (Finite Difference Methods, Monte Carlo methods), Exotic Options, Limitations of the Black-Scholes Theory - Imperfect Markets (Arbitrage Pricing and Equivalent Martingale Measures, Asset Price Models for which Arbitrage Pricing Fails, Transaction Costs) Textbooks: - "Dynamic Asset Pricing Theory", Third Edition. by Darrell Duffie - "Options, Futures, and Other Derivatives" (5th Edition) by John C. Hull - "Asset Pricing" by John H. Cochrane Complementary Text Book: - "The Mathematics of Financial Derivatives", by P. Wilmott, S. Howison and H. Dewynne, 1995, Cambridge University Press PART II. Term-Structure Models and Portfolio Theory Term-Structure Models: One-Factor Term-Structure Models, Cox-Ingersoll- Ross Model, Affine Single-Factor Models, Term-Structure Derivatives, Hedging, Green's Function and Term Structure, Multifactor Models, The Multifactor CIR Term-Structure Model, Mortgage Backed Securities, The Heath-Jarrow-Morton Model of Forward Rates Optimal Portfolio and Consumption Choice: Stochastic Control, Merton's Problem, Solution to Merton's Problem, The Infinite Horizon Case, The Martingale Solution, The Utility Gradient Approach Equilibrium: The Primitives, Security-Spot Market Equilibrium, Arrow- Debrew Equilibrium, Real Security Prices, Optimality with Additive Separable Utility, Equilibrium with Smooth-Additive Utility, The Consumption -Based CAPM, The CIR Term Structure, The CCAPM without Dynamic Spanning Textbook: - "Dynamic Asset Pricing Theory", Third Edition, by Darrell Duffie - "Stochastic Calculus for Finance II : Continuous-Time Models (Springer Finance)" by Steven E. Shreve - "Credit Risk : Pricing, Measurement, and Management (Princeton Series in Finance)" by Darrell Duffie, Kenneth J. Singleton Complementary Textbooks: - "Security Markets, Stochastic Models", by D. Duffie, 1988, Academic Press - "Continuous-Time Finance", by R. Merton, 1990, Blackwell PART III. Introduction to Risk Management and Financial Engineering Financial Optimization and Risk Management, Risk Indicators at Instrumental Level; (Single Fixed Flow, Fixed Rate Bond, FRA, Interest Rate Futures, Interest Rate Swaps, FX Spot, FX Forward, Plain Vanilla Options), Credit Risk, Risk Indicators at the Portfolio Level (Pricing Environment, Interest Rate Factors, FX Factors), Value-at-Risk (VAR) and Asset-Liability Management, Risk Metrics - Market Risk in a Single Position, Measures of Market Risk: (Linear and Non-linear Positions), Market Risk Limits, Calibrating Valuation and Risk Models Performance Evaluation, Probability Distributions and Statistical Assumptions Forecasting Volatilities and Correlations (Basic Design, Ex-post Estimation, Ex-ante Estimation - Forecasting, Defining the Optimal Decay Factor), Assessing Performance (Univariate and Multivariate Tail
10 Probabilities), Mathematics of Structures Monte Carlo (Generating Statistics, Properties of the Correlation Matrix), Mapping Algorithms (Fixed Income, Foreign Exchange, Commodities, Options). Textbooks: - "Financial Optimization" by Stavros A. Zenios - "Principles of Financial Engineering (Academic Press Advanced Finance)", by Salih N. Neftci - "Monte Carlo Methods in Financial Engineering (Stochastic Modelling and Applied Probability)" by Paul Glasserman Complementary Textbook: "Managing Financial Risk", by Charles W. Smithson and Clifford W. Smith, Jr, 1995, IRWI Prof. Igor Konnov, Kazan University, Via dei Caniana 2, Bergamo Monday 17 June 14,00-16,00 Room 22 Wednesday 19 June 14,00-17,00 Room 22 Thursday 20 June 14,00-17,00 Room 22 Friday 21 June 14,00-16,00 Room 22 Variational inequalities methods algorithms Seminar Right-hand side decomposition for variational inequalities Monday 24 June 9,30-10,30 Room 23 Prof. Florian Potra,Via dei Caniana 2, Bergamo Friday 21 June 16,00-19,00 Room 22 Tuesday 25 June 18,00-20,00 Room 22 Interior point method: its application in linear and non linear programming ICPS 2013 SP XIII From Monday 8 July to Friday 12 July Information at the following web site
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