B R O C H U R E D E I C O R S I

Transcript

1 Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche B R O C H U R E D E I C O R S I Corso di studio in Quantitative Finance and Insurance Printed by Campusnet - 16/08/ :43

2 Indice Indice APPLIED MATHEMATICS APPLIED MATHEMATICS ASSET PRICING AND PORTFOLIO CHOICE ASSET PRICING AND PORTFOLIO CHOICE BANKING BANKING COMMERCIAL LAW (ADVANCED) COMMERCIAL LAW (ADVANCED) CORPORATE FINANCE CORPORATE FINANCE DERIVATIVES DERIVATIVES ECONOMETRICS II ECONOMETRICS II ECONOMICS OF SAVINGS AND PENSIONS ECONOMICS OF SAVINGS AND PENSIONS FINANCE AND FINANCIAL ACCOUNTING - CORSO INTEGRATO FINANCE AND FINANCIAL ACCOUNTING - MODULO CORPORATE FINANCE Corporate Finance FINANCE AND FINANCIAL ACCOUNTING - MODULO FINANCIAL ACCOUNTING FINANCE AND INSURANCE ACCOUNTING - CORSO INTEGRATO FINANCE AND INSURANCE ACCOUNTING - MODULO INSURANCE ACCOUNTING FINANCE AND INSURANCE ACCOUNTING- MODULO CORPORATE FINANCE Corporate Finance FIXED INCOME FIXED INCOME LIFE AND NON-LIFE INSURANCE TECHNIQUES LIFE AND NON-LIFE INSURANCE TECHNIQUES MATHEMATICS FOR FINANCE MATHEMATICS FOR FINANCE MATHEMATICS FOR INSURANCE MATHEMATICS FOR INSURANCE NUMERICAL AND STATISTICAL METHODS FOR FINANCE NUMERICAL AND STATISTICAL METHODS FOR FINANCE SIMULATION MODELS FOR ECONOMICS SIMULATION MODELS FOR ECONOMICS STATISTICS II STATISTIC II

3 APPLIED MATHEMATICS APPLIED MATHEMATICS Codice attività didattica: SEM0023 Docenti: Di base Crediti/Valenza: 6 Italiano Obbligatoria Tipologia esame: Orale Mutuato da: Pagina web del corso:

4 ASSET PRICING AND PORTFOLIO CHOICE ASSET PRICING AND PORTFOLIO CHOICE Codice attività didattica: ECO0262 Corso di studio: Crediti/Valenza: 9 Tipologia esame: PREREQUISITI Giovanna Nicodano (Titolare del corso) o 5006, giovanna.nicodano@unito.it Finance Insurance and Statistics 1 anno Caratterizzante SECS-P/01 - economia politica Obbligatoria Scritto Fundamentals of calculus, statistics, econometrics, finance are prerequisites. Essential background material is found in the following textbook: Bodie Z., Kane A., Marcus A.J., Investments, McGraw Hill, International Edition, senza scheda S&P. cap. 5-11, 13 e OBIETTIVI FORMATIVI inglese This course focusses on asset pricing methods and quantitative investment management techniques. The first part deals with asset pricing theory. The second part addresses quantitative portfolio choice methods and their ex-post performance. Such methods account for investors' horizons, return predictability and estimation risk. The third part is devoted to some special topics. RISULTATI DELL'APPRENDIMENTO ATTESI inglese 1. Knowledge and understanding ability The first part of the course allows to recognize risk-based drivers of pricing in simple, static contexts. Based on the second part of the course, students will be able to address the following issues: 1. Why should investors diversify across assets? Which are relevant characteristics of asset classes? 2. How can a worker achieve a stable consumption flow during working years (given labor income risk) and during retirement? Is she saving enough for retirement? Should a worker reduce investment into stocks as retirement approaches? Which is the optimal asset allocation for a pension fund? 3. Is it possible to reliably predict the return on one asset? On a portfolio of assets? On the relative return of two - 3 -

5 assets?... Are stock returns more predictable over a day, a month, a year, a decade? Is it true that in efficient markets asset returns are unpredictable? 4. Do ex ante optimal portfolios perform better relative to simpler ones in ex post experiments? How large are gains from portfolio diversification across assets? 5. Are stocks safer in the long run? How large are gains from portfolio diversification over time? 6. Is it true that "alternative assets" increase the Sharpe ratio of portfolios? Are the returns on such assets similar to those of other assets? 2) Capability to apply knowledge and understanding The course enables to choose from a set of tools to cope with practical problems of risk assessment, portfolio management and asset pricing. For instance: 1. How to measure expected returns on different stocks on the basis of a small set of determinants. How to use existing assets to price redundant assets. How to identify arbitrage opportunities. 2. How to use asset pricing models to design long-short strategies? And portfolios with desired risk exposures. How to replicate a stock index? How to use asset pricing models to evaluate ex post performance of mutual funds? 3. How can a worker smooth consumption during working years (given labor income risk) and during retirement? Is she saving enough for retirement? Should a worker reduce investment into stocks as retirement approaches? Which is the optimal asset allocation for a pension fund? 4. Which techniques can a portfolio manager use to improve on ex- post performance? 5. How can we exploit predictability while optimizing the risk/return trade-off? 6. Can we use standard portfolio optimization tools to invest in alternatives? And what about ex-post performance measures: should we modify them to evaluate portfolios that include alternatives? 3) Capability to approach the subject in a critical manner This is a key challenge. The asset and risk management industry acts upon an evolving body of knowledge, so that the portfolio manager must be able to critically cope with new concepts and techniques. So as to train to this, we will present some unsettled issues - such as the possibility to exploit return predictability for improving portfolio performance -and the different actions to take depending on one's own critical assessment of the matter. We will also emphasize the difficulty in choosing to reduce risk taking when the asset manager's incentives are tilted towards maximizing short term returns. 4) Communication abilities Students are expected to solve three problem sets in randomly-formed teams. If time allows, random participants in each team will be asked to present some results. 5) Learning ability The reading list includes a variety of materials, from beginners' textbooks to technical hadbooks and scientific papers. This ought to teach how to refer to different sources, when necessary. Lecture notes ease the approach to complex sources. MODALITA' DI INSEGNAMENTO The course is based on both formal lectures and at least as many hours of at home - 4 -

6 reading and solving exercises. MODALITÀ DI VERIFICA DELL'APPRENDIMENTO A test will be taken during the first lecture, on the basis of Bodie Kane and Markus (see prerequisites). Weight 5-15%. A second test will be taken during the course, on a random date (weight 25-35%). A third test (weight 60%) will be taken after the end of the course ATTIVITÀ DI SUPPORTO Weekly office hours during the course. PROGRAMMA inglese Risk-based Asset Pricing 1. Pricing with the Stochastic Discount Factor 2. Efficient Frontier and CCAPM 3. Return Predictability and Market Efficiency 4. Contingent Claim Pricing 5. Risk Neutral Probabilities 6. Equilibrium pricing in complete markets Portfolio Choice 7. Human Capital, Life Cycle Saving and Investing 8. Return Predictability: Stylized Facts 9. Estimation risk and ex post performance of optimal portfolios. 10. Return Predictability and long term asset allocation Topics 11. Pricing votes 12. Pricing information 13. Investing in alternative assets 14. Governance-based portfolio strategies 15. Tax arbitrage Changes will be communicated at the beginning of the course. TESTI CONSIGLIATI E BIBLIOGRAFIA This reading list is indicative. The complete reading list wil be available on Moodle at the beginning of the course. It will comprise both book chapters and scientific papers

7 Cochrane J., Asset Pricing, Princeton University Press, 2001 Ch Campbell J.Y and L. M. Viceira, Strategic Asset Allocation, Oxford Un. Press, 2002, Ch. 6, Introduction; Ch ; Ch. 7 D- Lou, C. Polk, S. Skouras, A Tug of War: Overnight vs. Intraday Expected Returns, LSE Goyal A., and I. Welch, 2008, "A Comprehensive Look at The Empirical Performance of Equity Premium Prediction", Review of Financial Studies, 21(4), Jorion P., International Portfolio Diversification with Estimation Risk, Journal of Business, 58(3), 1985, Garlappi Uppal, 1/N, The Review of Financial Studies, 2009 Avramov D. and T. Chordia, Predicting Stock Returns, Journal of Financial Economics, Barberis N., Investing For the Long Run when Returns Are Predictable, Journal of Finance, Feb 2000 Pagina web del corso:

8 BANKING BANKING Codice attività didattica: SEM0018 Corso di studio: Crediti/Valenza: 9 Tipologia esame: PREREQUISITI OBIETTIVI FORMATIVI Alberto Eichholzer (Titolare del corso) Luca Martina (Titolare del corso) Prof. Giorgio Spriano (Titolare del corso) alberto.eichholzer@unito.it Finance 2 anno Caratterizzante SECS-P/11 - economia degli intermediari finanziari Facoltativa Orale RISULTATI DELL'APPRENDIMENTO ATTESI ATTIVITÀ DI SUPPORTO PROGRAMMA Pagina web del corso:

9 COMMERCIAL LAW (ADVANCED) COMMERCIAL LAW (ADVANCED) Codice attività didattica: SEM0016 Corso di studio: Crediti/Valenza: 6 Tipologia esame: PREREQUISITI OBIETTIVI FORMATIVI Marco Aiello (Titolare del corso) , marco.aiello@unito.it Finance Insurance and Statistics 2 anno Caratterizzante IUS/04 - diritto commerciale Italiano Facoltativa RISULTATI DELL'APPRENDIMENTO ATTESI ATTIVITÀ DI SUPPORTO PROGRAMMA Pagina web del corso:

10 CORPORATE FINANCE CORPORATE FINANCE Codice attività didattica: ECO0130 Corso di studio: Crediti/Valenza: 9 Tipologia esame: PREREQUISITI Prof. Vittorio De Pedys (Titolare del corso) vittorio.depedys@unito.it Finance 1 anno Caratterizzante SECS-P/08 - economia e gestione delle imprese Facoltativa Orale Mutuato da: Pagina web del corso:

11 DERIVATIVES DERIVATIVES Codice attività didattica: ECO0207 Corso di studio: Crediti/Valenza: 9 Tipologia esame: PREREQUISITI OBIETTIVI FORMATIVI Elisa Luciano (Titolare del corso) , elisa.luciano@unito.it Finance Insurance and Statistics 2 anno Caratterizzante SECS-S/06 - metodi matematici dell'economia e delle scienze att. e finanz. Italiano Facoltativa RISULTATI DELL'APPRENDIMENTO ATTESI ATTIVITÀ DI SUPPORTO PROGRAMMA Pagina web del corso: -

12 ECONOMETRICS II ECONOMETRICS II Codice attività didattica: ECO0143 Corso di studio: Finance 1 anno Caratterizzante Crediti/Valenza: 12 SECS-P/05 - econometria Facoltativa Tipologia esame: Orale Mutuato da: Pagina web del corso:

13 ECONOMICS OF SAVINGS AND PENSIONS ECONOMICS OF SAVINGS AND PENSIONS Codice attività didattica: ECO0154 Corso di studio: Crediti/Valenza: 6 Tipologia esame: PREREQUISITI OBIETTIVI FORMATIVI Elsa Maria Fornero (Titolare del corso) Mariacristina Rossi (Titolare del corso) elsa.fornero@unito.it Finance Insurance and Statistics 1 anno Affine o integrativo SECS-P/01 - economia politica Facoltativa Orale Apprendimento delle tecniche di base della ottimizzazione interetemporale. Conoscenza dei sistemi pensionistici a ripartizione e contributivi. RISULTATI DELL'APPRENDIMENTO ATTESI Padronanza dei concetti quali il risparmio e stock di ricchezza, processo di accumulazione e decumulazione, sistemi pensionistici MODALITA' DI INSEGNAMENTO Lezioni ed esercitazioni MODALITÀ DI VERIFICA DELL'APPRENDIMENTO Esame scritto e orale facoltativo ATTIVITÀ DI SUPPORTO Esercitazioni in laboratorio PROGRAMMA 1. Content and objectives Pension systems are designed to meet three main objectives: to allow people to smooth consumption in their life cycle; to prevent poverty in old age; to establish a compact among generations. These goals, in their turn, are meant to insure individual risk, to overcome individual planning limitations and to provide some sharing for aggregate risks. Within the first category of risks, longevity and earnings risks are predominant;

14 within the second, myopia and time inconsistency have to be addressed; within the third, demographic, economic and political risks should be as much diversified as possible. Starting from this framework, the course aims at placing European pension systems and reforms in the context of the economic theory of households' savings, where imperfect and incomplete (financial and insurance) markets make room for the state to play an insurer's role, besides its traditional redistributive tasks. The logic behind the "insurance perspective" does not imply giving up the traditional objective of solidarity, both within and between generations; indeed, this aim is strengthened by highlighting the key role of risk diversification. Furthermore, thanks to an analytical framework based on insurance, measures aimed at achieving a given distributional goal are easily designed; while, if the insurance framework is ignored, redistribution in practice ends up with unforeseen and undesirable features. 2. Learning outcomes 1) Knowledge and understanding Economic and psychological determinants of savings; functioning of both public and private pension systems; incentive and redistributive effects of pension systems. 2) Applying knowledge and understanding Application are possible to both simulation and econometric models. 3) Making judgments Improving the ability to understand the economic determinants of savings, to evaluate the costeffectiveness of different insurance programs, to compare the cost of different saving products. 4) Communication skills To acquire greater precision of concepts and language and to learn the economics behind welfare programs 5) Learning skills For a successful in learning, students must acquire a good familiarity with economic, financial and risks concepts 3. Covered topics are: i. Microeconomic foundations of retirement savings Basic deterministic saving models: the LCH and the PIH (intertemporal optimization models: assumptions and main results) Introducing uncertainty Certainty Equivalence Permanent Income Hypothesis Euler Equation Precautionary savings Life uncertainty and its effects. The introduction of (actuarially fair) life insurance and the dominance of annuities Why is the market for annuities everywhere so thin? Why are reverse mortgages almost ignored? ii. An economic analysis of social security (micro and macroeconomic features of social security) Financing mode: PAYG vs. Funding Pension formulae (DB vs. DC) Actuarial fairness and neutrality Measures of financial sustainability Measures of adequacy Redistribution (both within and between generations) Incentive structure (Induced) retirement The aggregate pension wealth (debt) iii. Theoretical and empirical models of retirement Stylised facts about retirement Determinants of retirement choice The implicit tax on postponing retirement (and related measures) iv. The economics of pension reforms and the importance of Economic-Financial Literacy A political economic approach to social security Assessing the political sustainability of social security reforms EFL: concept, measurement, stylized facts, consequences of illiteracy 4. Course organization Lectures, followed by discussions, and possibly a written composition at the end of the course. 5. Minimum requirements Basic quantitative and economic courses (microeconomics and public finance); Attendance of lectures 6. Selected Readings (Students may select one or two according to their specific interests) TESTI CONSIGLIATI E BIBLIOGRAFIA 1. Browning, M., A. Lusardi, 1996, "Household Saving: Micro Theories and Micro Facts", Journal of Economic Literature, 34, Barr N, P. Diamond, Reforming Pensions, 3. Coronado J. L., D. Fullerton, T. Glass, 1999, "Distributional Impacts of Proposed Changes to the Social Security System in Tax Policy and the Economy, Vol. 13, Poterba, Jim, ed., 1999, pp Diamond P. and P. Orszag, 2004, Saving Social Security. A Balanced Approach, Brookings Institution Press, Washington DC. 5. Diamond Peter, 2005, "Social Security Rules that Vary with Age", in: Fornero, E. and P. Sestito (eds), 2005, Pension Systems: Beyond Mandatory Retirement, Cheltenham: Edward Elgar. 6. Diamond, P. 2004, 'Social Security', The American Economic Review, 94(1), March Disney, R., "Actuarialbased public pension systems", in: G. Clark, A. Munnell and M. Orszag, The Oxford Handbook of Pensions and Retirement Income, OUP, Fenge R. and Pestieau P., 2005, "Social Security and Early Retirement", Cesifo Book Series, the MIT Press. 9. French E, 2005, The Effects of Health, Wealth and Wages on the Labour Supply and Retirement, Review of Economic Studies, vol 72, no 2, Aprile, Fornero E, A Lusardi, C Monticone, Adequacy of Saving for Old

15 Age in Europe, prepared for the ESF Forward Look project Ageing, Health and Pensions in Europe (the Hague, April 22nd, 2009) 11. Fornero E., Economic-financial literacy and (sustainable) pension reforms: why the former is a key ingredient for the latter, Bankers, Markets & Investors, 134, January-February Geanakoplos J., O.S. Mitchell, S. P. Zeldes, 1998, "Social Security Money's Worth", PaineWebber WP Series in Money, Economics and Finance 98-05, Columbia Business School, August. 13. Gourinchas P.O., Parker J., 2002, "Consumption over the life cycle" Econometrica, vol. 70, no 1 (January, Gruber J., D. Wise (eds.), 1999, Social Security and Retirement Around the World, Chicago: University of Chicago Press. 15. Lindbeck A. and M. Persson, 2003, "The Gains from Pension Reform", Journal of Economic Literature, vol. 41 (1), pp Mitchell O. S., S. P. Zeldes, 1996, "Social Security Privatization: a Structure for Analysis", American Economic Review, 86(2), pp: Scholtz K. Seshadri A., Khitatrakun S., 2006, "Are Americans Saving "Optimally" for Retirement?" Journal of Political Economy, 114(4), pp Additioanl Material will be uploaded into Dropbox folder NOTA Verranno distribuite slide e materiale aggiuntivo a lezione Pagina web del corso:

16 FINANCE AND FINANCIAL ACCOUNTING - CORSO INTEGRATO Codice attività didattica: SEM0019 Corso di studio: Crediti/Valenza: 12 Tipologia esame: PREREQUISITI OBIETTIVI FORMATIVI Insurance and Statistics 1 anno Caratterizzante SECS-P/07 - economia aziendale SECS-P/08 - economia e gestione delle imprese Facoltativa RISULTATI DELL'APPRENDIMENTO ATTESI ATTIVITÀ DI SUPPORTO PROGRAMMA Pagina web del corso: -

17 FINANCE AND FINANCIAL ACCOUNTING - MODULO CORPORATE FINANCE Corporate Finance Codice attività didattica: SEM0019A Corso di studio: Insurance and Statistics 1 anno Di base Crediti/Valenza: 6 SECS-P/08 - economia e gestione delle imprese Facoltativa Tipologia esame: Orale Mutuato da: Pagina web del corso: -

18 FINANCE AND FINANCIAL ACCOUNTING - MODULO FINANCIAL ACCOUNTING Codice attività didattica: SEM0019B Corso di studio: Insurance and Statistics 1 anno Di base Crediti/Valenza: 6 SECS-P/07 - economia aziendale Italiano Obbligatoria Tipologia esame: Orale Mutuato da: Pagina web del corso: -

19 FINANCE AND INSURANCE ACCOUNTING - CORSO INTEGRATO Codice attività didattica: SEM0045 Corso di studio: Crediti/Valenza: 12 Tipologia esame: PREREQUISITI OBIETTIVI FORMATIVI Insurance and Statistics 1 anno Caratterizzante SECS-P/07 - economia aziendale SECS-P/09 - finanza aziendale Facoltativa RISULTATI DELL'APPRENDIMENTO ATTESI ATTIVITÀ DI SUPPORTO PROGRAMMA Pagina web del corso: -

20 FINANCE AND INSURANCE ACCOUNTING - MODULO INSURANCE ACCOUNTING Codice attività didattica: SEM0045A Corso di studio: Crediti/Valenza: 6 Tipologia esame: PREREQUISITI Insurance and Statistics 1 anno Di base SECS-P/07 - economia aziendale Italiano Obbligatoria Orale Mutuato da: Pagina web del corso: -

21 FINANCE AND INSURANCE ACCOUNTING- MODULO CORPORATE FINANCE Corporate Finance Codice attività didattica: SEM0045B Corso di studio: Crediti/Valenza: 6 Tipologia esame: PREREQUISITI OBIETTIVI FORMATIVI Insurance and Statistics 1 anno Di base SECS-P/09 - finanza aziendale Facoltativa RISULTATI DELL'APPRENDIMENTO ATTESI ATTIVITÀ DI SUPPORTO PROGRAMMA Pagina web del corso: -

22 FIXED INCOME FIXED INCOME Codice attività didattica: SEM0021 Corso di studio: Crediti/Valenza: 6 Tipologia esame: PREREQUISITI OBIETTIVI FORMATIVI Marina Marena (Titolare del corso) Luca Martina (Titolare del corso) , marina.marena@unito.it Insurance and Statistics 2 anno Caratterizzante SECS-S/06 - metodi matematici dell'economia e delle scienze att. e finanz. Facoltativa Scritto english Valuation of fixed income instruments. RISULTATI DELL'APPRENDIMENTO ATTESI english Being familiar with fixed-income markets and instruments. MODALITA' DI INSEGNAMENTO english Lectures and lab sessions. MODALITÀ DI VERIFICA DELL'APPRENDIMENTO english 50% coursework and 50% examination. PROGRAMMA english BOND ANALYSIS: - Bond definition and characteristics - Bond types - Bond structure and priority - Bond valuation - Bond Return Measures (CY, YTM, YTC) - Yield curve

23 - The effect of interest rate changes on bond prices - Duration - Determinants of Interest Rates - Bond ratings and CRAs - Bond spread - Bond Yields - Government Bonds PORTFOLIO MANAGEMENT: - Portfolio competition and market/strategy comments FIXED INCOME DERIVATIVES: - Fixed-income derivatives - Bootstrap of the interest rate curve - Interest rate models TESTI CONSIGLIATI E BIBLIOGRAFIA english Material and lecture notes will be made available via Moodle. References for FIXED INCOME DERIVATIVES: Brigo, D., Mercurio, F., Interest Rate Models: Theory and Practice With Smile, Inflation and Credit, Springer, Kienitz, J., Interest Rate Derivatives Explained, Palgrave Macmillan, NOTA The course should be taken together with "Derivatives". Pagina web del corso:

24 LIFE AND NON-LIFE INSURANCE TECHNIQUES LIFE AND NON-LIFE INSURANCE TECHNIQUES Codice attività didattica: SEM0020 Corso di studio: Crediti/Valenza: 12 Tipologia esame: PREREQUISITI OBIETTIVI FORMATIVI Gabriele Pieragnoli (Titolare del corso) Insurance and Statistics 2 anno Caratterizzante SECS-S/06 - metodi matematici dell'economia e delle scienze att. e finanz. Obbligatoria RISULTATI DELL'APPRENDIMENTO ATTESI ATTIVITÀ DI SUPPORTO PROGRAMMA Pagina web del corso:

25 MATHEMATICS FOR FINANCE MATHEMATICS FOR FINANCE Codice attività didattica: ECO0165 Corso di studio: Crediti/Valenza: 9 Tipologia esame: PREREQUISITI Bertrand Lods (Titolare del corso) Gabriele Pieragnoli (Titolare del corso) bertrand.lods@unito.it Finance Insurance and Statistics 1 anno Caratterizzante SECS-S/06 - metodi matematici dell'economia e delle scienze att. e finanz. Obbligatoria Scritto english A good knowledge of basic calculus (Matematica Generale), of the foundations of probability calculus and statistical infererence (Statistica) OBIETTIVI FORMATIVI english This course is a 2 module course (9 credits) aimed at introducing and developing many of the mathematical tools which are used in applied finance and insurance. ln this module, particular stress will be posed on the development of the measure theoretical tools and advanced probability concepts with emphasis on their applications to investment and insurance decisions. RISULTATI DELL'APPRENDIMENTO ATTESI english At the end of the course, the student is expected to be capable of: - using the basic tools and results to pose, formalize and solve a probability problem models of applied interest. The introduction of stochastic processes and their properties is always motivated by the wish to develop models for observed phenomena. - knowing the extent to which the results obtained in the previous step are de pendent on the assumption that s/he has made about the behavior of the economic agents

26 - being able to think about possible and useful generalizations of the model - being able to communicate such findings using appropriate and clear mathematical notation and language MODALITA' DI INSEGNAMENTO The course is articulated in 72 hours of formal in class lecture time, and in at least as many hours of at home work solving practical exercises. MODALITÀ DI VERIFICA DELL'APPRENDIMENTO The course grade is determined solely on the basis of a written examination. The examination (2 hours and 45 minutes) test the student's ability to do the following: Present briefly the main ideas, concepts and results developed in the course, also explaining intuitively the meaning and scope of the definitions and the arguments behind the validity of the results Use effectively the concepts and the result to answer questions in basic measure theory and stochastic process theory, e.g. computing the Ito integral of some given stochastic process. The above is accomplished by asking the student to answer 5 6 questions. Each of the questions has an essay part, and some of the questions also have a more practical ("exercise ") part. ATTIVITÀ DI SUPPORTO english Weekly homework sets will be assigned, and their solution will be posted and (if time allows) discussed in class PROGRAMMA english The course is divided into two parts: Part 1: Measure, Probability and basics of decision making (Ghirardato) - Foundations of measure theory. Measures, measurable functions, Lebesgue integrals, Lp spaces, theorems of Fubini and Radon-Nikodym -Applications of measure theory to probability calculus. Conditional probabilities and expectation, filtrations Part 2: Stochastic Processes (Lods) -Martingales and their convergence -Markov chains -The Poisson process: construction and properties. Some examples -Probability measures on real-valued function spaces. The Wiener measure -Brownian motion: construction and properties. Variation in Brownian motion TESTI CONSIGLIATI E BIBLIOGRAFIA The following are the required textbooks for the course: -M. Capinski e E. Kopp, Measure, Integral and Probability, Second Edition, Springer-Verlag, Berlino, Z. Brzezniak and T. Zastawniak, Basic Stochastic Processes, Springer-Verlag, Berlino, Pagina web del corso:

27 MATHEMATICS FOR INSURANCE MATHEMATICS FOR INSURANCE Codice attività didattica: ECO0166 Corso di studio: Crediti/Valenza: 6 Tipologia esame: PREREQUISITI Prof. Giulio Diale (Titolare del corso) , giulio.diale@unito.it Insurance and Statistics 1 anno Caratterizzante SECS-S/06 - metodi matematici dell'economia e delle scienze att. e finanz. Facoltativa Scritto ed orale Non vi sono prerequisiti formali, ma è opportuno che lo studente possegga i concetti di base del calcolo finanziario e del calcolo delle probabilità. English There are no formal prerequisites, but it is advisable that the students are familiar with the introductory financial calculus and the theory and calculus on probability OBIETTIVI FORMATIVI Il corso si propone di introdurre i concetti di base della Matematica per Assicurazioni, che, oltre alla matematica attuariale impiegata nel calcolo dei premi e delle riserve matematiche del ramo vita, include i modelli di caricamento di sicurezza dei premi, inquadrabili nel teoria dell'utilità attesa ed i modelli di valutazione delle prestazioni assicurative nel ramo danni. English The main purpose is to introduce Insurance Mathematics, life and non-life, providing a general foundation to the mathematics of the insurance business, in which probability, individuals' and companies' behaviour towards risk plays a fundamental role. Financial considerations are also important, as they affect life insurance policy choices. RISULTATI DELL'APPRENDIMENTO ATTESI Conoscenza e comprensione Conoscenza di base di modelli matematici impiegabili nelle assicurazioni vita e non vita, capacità di interpretazione delle conseguenze matematiche della maggior parte delle clausole di un contratto di assicurazione. Capacità di applicare conoscenza e comprensione. Abilità a tradurre in formule matematiche i diversi contratti assicurativi e valutare gli impegni delle controparti di un contratto. Saper sviluppare i calcoli attuariali anche su supporto informatico. Autonomia di giudizio Lo studente deve saper riconoscere nei diversi contratti gli aspetti attuarialmente fondati da quelli non inquadrabili in una teoria coerente. Abilità comunicative. Lo studente deve saper impiegare correttamente in forma scritta il complesso simbolismo

28 della teoria e saperla anche decodificare, ossia, di fronte ad una formula, saper riconoscere le prestazioni sottostanti. Capacità di apprendimento. Le abilità acquisite permettono allo studente di completare la propria preparazione nei diversi aspetti della pratica assicurativa, inserendosi proficuamente in ogni ambiente di lavoro rivolto ai problemi attuariali. English Knowledge and understanding Basic knowledge of mathematical modelling in life and non life insurance, ability to interpret most insurance policies from a mathematical point of view. Applying knowledge and understanding Ability to convert various policies into formulas, and to assess what is due by the counterparts of an insurance policy. Ability to implement actuarial formulas on a PC. Making judgements Students will be able to discern the different aspects in an insurance policy, whether actuarially founded or not. Communication skills Students will properly use in written expression the symbols of insurance mathematics, and will be able to interpret them (i.e., looking at a formula, be able to recognise the underlying facts). Learning skills The skills acquired will give students the opportunity of improving and deepening their knowledge of the different aspects of the practice of insurance. They will thus move comfortably in any work environment dealing with insurance problem-solving. MODALITA' DI INSEGNAMENTO Italiano Lezioni ed esercitazioni frontali. English Front lectures and class work MODALITÀ DI VERIFICA DELL'APPRENDIMENTO Italiano L'apprendimento è verificato attraverso l'esame finale, che si svolge mediante una prova scritta con due esercizi, uno del ramo danni, l'altro sul ramo vita. Coloro che riportano una valutazione sufficiente di almeno 18/30 possono sostenere il colloquio orale, che verte su aspetti concettuali e sulla verifica della conoscenza della terminologia in uso nella pratica assicurativa e dei modelli matematici impiegati. English The learning is checked in the final exam, consisting of a written test, where there are two exercises, one on non-life insurance mathematics, the other one on life insurance mathematics. Those who get a mark greater o equal to 18/30 can have an oral on the theory about the implementation of the insurance mathematical models we can find in practice. PROGRAMMA Tipi di coperture assicurative. Assicurazioni contro i danni. Concetto di premio assicurativo. Sinistri, danni, risarcimenti. Caricamenti e premi di tariffa