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MATHEMATICS FOR FINANCE
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MATHEMATICS FOR FINANCE
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Academic year 2016/2017
- Course ID
- SEM0065
- Teaching staff
- Bertrand Lods (Titolare del corso)
Marina Marena (Titolare del corso) - Degree course
- Finance
Insurance and Statistics - Year
- 1° anno
- Teaching period
- Primo semestre
- Type
- Caratterizzante
- Credits/Recognition
- 12
- Course disciplinary sector (SSD)
- SECS-S/06 - metodi matematici dell'economia e delle scienze att. e finanz.
- Delivery
- Tradizionale
- Language
- Inglese
- Attendance
- Obbligatoria
- Type of examination
- Scritto
- Prerequisites
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A good knowledge of basic calculus (Matematica Generale), of the foundations of probability calculus and statistical infererence (Statistica)
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Sommario del corso
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Course objectives
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. The introduction of stochastic processes and their properties is always motivated by the wish to develop models for observed phenomena.- Oggetto:
Results of learning outcomes
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 of applied interest
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knowing the extent to which the results obtained in the previous step are dependent on the assumption that s/he has made about the behavior of the economic agents
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being able to think about possible and useful generalizations of the model
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being able to communicate such findings using appropriate and clear mathematical notation and language
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Course delivery
Location: https://www.finance-insurance.unito.it/robots.htmlThe course is articulated in 63 hours of formal in‐class lecture time, and in at least as many hours of at‐home work solving practical exercises.- Oggetto:
Learning assessment methods
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
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Use effectively the concepts and the results 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.
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Support activities
Weekly homework sets will be assigned, and their solution will be posted and (if time allows) discussed in class- Oggetto:
Program
The course is divided into two parts:Part 1: Measure, Probability and basics of decision making (Lods)-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, filtrationsPart 2: Stochastic Processes (Marena)-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 motionSuggested readings and bibliography
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The following are the required textbooks for the course:Part I- Capinski, Kopp (2005). Measure, Integral and Probability, Second Edition, Springer-Verlag.Part II- Brzezniak, Zastawniak (1999). Basic stochastic processes, Springer.
- Capiński, Kopp, Traple (2012). Stochastic Calculus for Finance, Cambridge University Press.- Björk (2009). Arbitrage theory in continuous time, Oxford University Press.
- Lamberton, Lapeyre (2007). Introduction to stochastic calculus applied to finance, Chapman and Hall.- Mikosch (1998). Elementary stochastic calculus with finance in view, World Scientific.
- Oksendal (2010). Stochastic differential equations, Springer.- Shreve (2004). Stochastic calculus for finance I & II, Springer.
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Class schedule
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