## FINANCIAL MATHEMATICS II MATEMATICA FINANZIARIA II

#### Financial Mathematics II Matematica Finanziaria II

A.Y. Credits
2015/2016 8
Lecturer Email Office hours for students
Laura Gardini

### Assigned to the Degree Course

Date Time Classroom / Location

### Learning Objectives

The course aims to complete the preparation provided by the basic course, introducing new assessment tools for financial flows and bonds (financial immunization techniques). We then introduce some basic elements for the estimation and evaluation of financial transactions within uncertainty (or risky). The mathematic subjects include some properties of functions of several variables, and elements of free and constrained optimization. These properties are applied to the problem of selecting an optimal portfolio of risky assets

### Program

Part A
Elements of bond portfolio management: Consistency Market Hypothesis (or absence of arbitrage). Term structure, spot rates and forward rates. Evaluation of the term structure. Estimate of the yield curve using spot rates. Structure of interest rates and spot prices. Evaluation of Bonds. Volatility estimate of the present value. Implici Interest Reate of a financial flow. Volatility of the value function and Duration. Its use in immunization techniques.

Part B
Unconstrained classical optimization. Least squares Method. Convex Functions, Quadratic forms with linear constraints. Convex optimization. Optimization with Equality Constraints. Portfolio at minimal risk. Sensitivity Analysis.

Part C
Evaluation Criteria in uncertainty conditions. Average Value criterion. Paradox of St. Petersburg. Criterion of Expected utility. Risk Propension/Aversion. Some examples of utility functions. Mean-variance criterion (M-V). Risk-return analysis. Indifference curves.
Portfolio Theory. Returns as normal random variables. Portfolio of two risky assets. Variance of a portfolio of two risky assets. Case of perfect positive / negative correlation. Uncorrelated returns. Generic correlation value. Selection of an optimal portfolio with n risky assets. Properties of the efficient frontier. Portfolios that include a riskless asset. Portfolios with one risky and one riskless asset. . Portfolios with n risky and one riskless assets (CAPM, Capital Asset PricingModel). Separation theorem.

### Learning Achievements (Dublin Descriptors)

Students are expected to acquire knowledge and understanding in applied mathematics to the theory of portfolio of risky assets and elements useful in the evaluation of flows also under uncertainty and risk, so to get a proper knowledge suitable for autonomy in working environments in the financial sector. In addition to a good learning ability, it is expected the ability to apply the acquired knowledge in autonomous and competent way.

### Teaching Material

The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it

### Teaching, Attendance, Course Books and Assessment

Course books

Modern portfolio theory and investment analysis. E.J. Elton and M.J. Gruber, J. Wiley and Sons, USA, Any edition. Chapters 1-21

Assessment

Oral examination

Disabilità e DSA

Le studentesse e gli studenti che hanno registrato la certificazione di disabilità o la certificazione di DSA presso l'Ufficio Inclusione e diritto allo studio, possono chiedere di utilizzare le mappe concettuali (per parole chiave) durante la prova di esame.

A tal fine, è necessario inviare le mappe, due settimane prima dell’appello di esame, alla o al docente del corso, che ne verificherà la coerenza con le indicazioni delle linee guida di ateneo e potrà chiederne la modifica.

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