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MATHEMATICAL MODELS FOR INVESTMENT DECISIONS Single discipline educational activity
Course Sheet Academic Year of enrolment:
Disciplinary Sector:
MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES
Professor and Collaborators:
Hours of classroom activity:
Prerequisites:
No specific foundation course is required but only some notions of probability theory, stochastic processes and financial mathematics.
Objectives
Contents - Investment Decisions under certainty
- Investment decisions under uncertainty
- Utility functions and their shapes
- The efficiency analysis of investments under uncertainty: stochastic dominance rules
- Investment valuation
- Real Options
Extended Syllabus Investment Decisions under certainty: the investment schedule, the meaning of indifference curves, optimal investment-consumption decisions, the money market line, separation of investment and financing decisions, finding the optimal investment, investment in securities under certainty.
Investment decisions under uncertainty: the nature of risk, the maximum return criterion, the maximum expected return criterion, the modern utility theory, alternative attitudes toward risk, the case of a linear utility function.
Utility functions and their shapes: partial information on preferences and decision-making, the Friedman-Savage hypothesis, the subjective utility approach, decreasing absolute risk aversion, risk attitudes in the stock market.
The efficiency analysis of investments under uncertainty: and stochastic dominance rules: the concept of an efficiency criterion, first degree stochastic dominance, second degree stochastic dominance, third degree stochastic dominance, efficiency criteria and diversification, the effectiveness of stochastic dominance criteria.
Investment valuation: investment valuation and risk importance, static and dynamic NPV, hints about stochastic NPV, mean-variance approach, stochastic dominance approach.
Real Options: a comparison between real and financial options, retrieval of Black and Scholes model and of the binomial model. Different approaches to the valuation of real options: classic, subjective, MAD, revised classic, integrated, DM method, Fuzzy number approach. Examples and applications.
Recommended Bibliography Portfolio and investment selection: theory and practice (from chapter 3 to 6) by Haim Levy and Marshall Sarnat
Teaching material provided by the teacher
Methods of Provision
Teaching Methods classroom-taught lesson where both theoretical and practical aspects of the discipline are dealt with eventually also with the use of Matlab.
Evaluation methods Verification of learning:
The exam is oral and may include the preparation of a project. The questions concern both the theory and the exercises and are aimed at verifying the preparation of the students on the topics in the program.
Contacts/More Information Student reception:
- 2 hours per week with dates and times communicated at the beginning of the course;
- on request by reservation via e-mail.