# STATISTICAL SCIENCES FOR FINANCE | Actuarial Mathematics and Mathematical Finance

## STATISTICAL SCIENCES FOR FINANCE Actuarial Mathematics and Mathematical Finance

 0222400012 DEPARTMENT OF ECONOMICS AND STATISTICS EQF7 STATISTICAL SCIENCES FOR FINANCE 2022/2023

 OBBLIGATORIO YEAR OF COURSE 1 YEAR OF DIDACTIC SYSTEM 2014 AUTUMN SEMESTER
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY SECS-S/06 10 60 LESSONS COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
 MARILENA SIBILLO T
ExamDate
MATEMATICA ATTUARIALE E FINANZA MATEMAT30/05/2023 - 11:30
MATEMATICA ATTUARIALE E FINANZA MATEMAT27/06/2023 - 11:30
MATEMATICA ATTUARIALE E FINANZA MATEMAT08/09/2023 - 11:30
Objectives
THE ACTUARIAL MATHEMATICS AND MATHEMATICAL FINANCE COURSE, IN LINE WITH THE CORE OBJECTIVES OF THE DEGREE PROGRAM, IS DEVOTED TO MATHEMATICAL MODELS USEFUL IN SOLVING ACTUARIAL AND FINANCIAL PROBLEMS. IN PARTICULAR, STUDENTS WILL LEARN HOW SELECT AND USE MATHEMATICAL METHODS FOR SOLVING PROBLEMS RELATED TO THE CONSTRUCTION OF EQUITY PORTFOLIOS, THE USE OF DERIVATIVE INSTRUMENTS, AND INSURANCE COVERAGE OF LIFETIME RISKS.
KNOWLEDGE AND UNDERSTANDING
THE KNOWLEDGE PROVIDED DURING THE COURSE WILL BE USEFUL TOOLS THAT STUDENTS WILL BE ABLE TO APPRECIATE NOT ONLY FOR THE THEORETICAL CONTENT BUT ALSO FOR THE APPLICATION PURPOSE OF EACH TOPIC TREATED, WHICH WILL ALWAYS BE CHARACTERIZED BY THE CONJUGATION OF THESE TWO ASPECTS. THE MODELS WILL ALL BE TREATED WITH THE AIM OF STIMULATING SCIENTIFIC CURIOSITY AND CRITICAL SKILLS OF STUDENTS. IN SUMMARY, THE CORNERSTONES OF THE COURSE WILL CONSIST OF THE FOLLOWING POINTS:
•CONSTRUCTION OF EQUITY PORTFOLIOS IN ACCORDING TO INVESTORS' EXPECTATIONS
•UNDERSTANDING OF THE THEORY BEHIND THE FUNCTIONING OF FINANCIAL MARKETS
•DERIVATIVES AS RISK CONTROL TOOLS
•UTILITY THEORY APPLIED TO THE INSURER-INSURED RELATIONSHIP
•MATHEMATICAL MODELS UNDERLYING THE PRICING OF LIFE INSURANCE COVERS AND THE MANAGEMENT OF LIFE INSURANCE PORTFOLIOS.
ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING
THE QUANTITATIVE TOOLS PRESENTED AND COMMENTED UPON DURING THE COURSE WILL ENABLE STUDENTS TO:
•BUILD FINANCIAL PORTFOLIOS BY MAXIMIZING EXPECTED RETURNS AND MINIMIZING RISK
•APPLY THE THEOREMS AND RESULTS OF FINANCIAL MARKET THEORY TO DEVELOP OPTIMAL STRATEGIES FOR MANAGING FINANCIAL PORTFOLIOS
•PRICING FINANCIAL DERIVATIVES AND USE THEM IN SPECULATIVE AND ARBITRAGE STRATEGIES
•CONTROL THE RISKS THAT IMPACT ON LIFE INSURANCE CONTRACTS AND MANAGE THE PROVISIONS AND PROFITS OF LIFE INSURANCE PORTFOLIOS.
TRANSVERSAL SKILLS
STUDENTS WILL ACQUIRE CRITICAL SKILLS THAT, APPLIED IN THE QUANTITATIVE FIELD, WILL BE USEFUL IN
•MAKE DECISIONS IN THE CONTEXT OF CHOICES TO BE MADE IN THE FINANCIAL-INSURANCE FIELD
•COMMUNICATE THE CONTENTS OF A FINANCIAL AND/OR ACTUARIAL ANALYSIS IN A CONCISE, SIMPLE YET RIGOROUS MANNER
•UNDERSTAND SPECIALIZED AND ADVANCED TOPICAL DOCUMENTS IN THE FINANCIAL AND INSURANCE FIELD
Prerequisites
MATHEMATICAL METHODS FOR ECONOMICS, FINANCIAL MATHEMATICS (I MODULE OF THE QUANTITATIVE METHODS COURSE), AND STATISTICS ARE RECOMMENDED.

Contents
THE ACTUARIAL MATHEMATICS AND MATHEMATICAL FINANCE COURSE CONSISTS OF TWO MODULES:
MODULE I - MATHEMATICAL FINANCE - 30 HOURS OF LECTURE WITH SOLUTION OF EXERCISES AND APPLICATIONS FOR EACH TOPIC.
THE MARKOWITZ MODEL. TOBIN'S MODEL. THE SINGLE-INDEX MODEL. THE CAPM. THE ARBITRAGE PRICING THEORY. EXAMPLES AND EXERCISES. FUTURES. THE OPERATORS IN THE FUTURES MARKET. PRICE. THE HEDGE RATIO. EXAMPLES AND EXERCISES. FINANCIAL OPTIONS. EUROPEAN CALL AND PUT OPTION. LIMITATIONS, STRATEGIES, RELATIONSHIPS. PRICING OF A EUROPEAN OPTION: THE BINOMIAL MODEL, THE BLACK-SCHOLES FORMULA. EXAMPLES AND EXERCISES. THE VALUE AT RISK FOR FINANCIAL PORTFOLIOS. EXAMPLES AND EXERCISES.
MODULE II - ACTUARIAL MATHEMATICS - 30 HOURS OF LECTURE WITH SOLUTION OF EXERCISES AND APPLICATIONS FOR EACH TOPIC.
THE UTILITY FUNCTION AND ACTUARIAL APPLICATIONS. THE POINT OF VIEW OF THE INSURED AND THE INSURER. EXAMPLES AND EXERCISES. THE "PRICE" OF A FINANCIAL TRANSACTION - RANDOM LIFE SPAN OF A PERSON. LIFE INSURANCE. PREMIUMS AND PRICES OF A LIFE INSURANCE COVERAGE. INSURANCE ON GROUPS OF PERSONS. THE MATHEMATICAL RESERVE. ASSESSMENT OF PROFIT. FLEXIBILITY OF BENEFITS. THE VALUATION OF LIABILITIES: THE FAIR VALUE. EXERCISES AND APPLICATIONS ON THE VARIOUS TOPICS COVERED.

THE DETAILED PROGRAM OF THE COURSE IS AVAILABLE ON THE TEACHER'S WEBSITE
Teaching Methods
THE COURSE OF ACTUARIAL MATHEMATICS AND MATHEMATICAL FINANCE CONSISTS OF 60 HOURS OF CLASSROOM TEACHING. LECTURES WILL BE FRONTAL AND CARRIED OUT WITH CONSTANT ATTENTION TO APPLICATIONS AND EXERCISES, WHICH WILL BE CARRIED OUT AT THE SAME TIME AS THE THEORETICAL TOPICS ARE DISCUSSED.

Verification of learning
THE VERIFICATION OF LEARNING IS ORIENTED TO STIMULATE THE STUDY AND STUDENTS' UNDERSTANDING OF THE TOPICS COVERED, WITH PARTICULAR ATTENTION TO THE ABILITY TO APPLY THE MODELS TO CONCRETE SITUATIONS.
THE FINAL EVALUATION OF THE STUDENT WILL CONSIST OF A WRITTEN TEST AND AN ORAL TEST FOR THE FIRST MODULE. EACH MODULE WILL BE CONSIDERED PASSED IF BOTH THE WRITTEN TEST AND THE ORAL TEST WILL HAVE OBTAINED AN EVALUATION AT LEAST SUFFICIENT. THERE WILL BE WRITTEN AND ORAL TESTS AT THE END OF EACH MODULE, IN ADDITION TO THE SESSIONS SCHEDULED IN THE DEPARTMENT'S CALENDAR. EACH TEST FOR EACH MODULE WILL BE EVALUATED IN THIRTIETHS: EACH MODULE WILL BE EVALUATED BY MAKING THE ARITHMETIC AVERAGE OF THE EVALUATIONS OBTAINED FOR THE WRITTEN AND FOR THE ORAL AND THE FINAL GRADE WILL BE THE AVERAGE OF THE EVALUATIONS OBTAINED FOR THE TWO MODULES.
THE WRITTEN TEST, FOR BOTH MODULES, WILL HAVE A STRONG APPLICATIVE AND PRACTICAL CHARACTERIZATION. THE ORAL TEST WILL BE THEORETICAL.

Texts
A. OLIVIERI, E.PITACCO, 2011, INTRODUCTION TO INSURANCE MATHEMATICS, SPRINGER
D. G. LUENBERGER, 2009, INVESTMENT SCIENCE, OXFORD UNIVERSITY PRESS (SECOND EDITION)
P. WILMOTT, 2007, PAUL WILMOTT INTRODUCES QUANTITATIVE FINANCE, THE WILEY FINANCE SERIES

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