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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:
CAROLI COSTANTINI Cristina
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 Stochastic control of diffusion processes and applications in finance. Introduction to interest rate models.
Extended Syllabus Stochastic control of diffusion processes, both with finite and infinite horizon.
The Hamilton-Jacobi-Bellman equation and the verification theorem.
Optimal strategies for some investement decision problems: Merton's problem of optimal portfolio allocation; the reinsurance problem; investment/consumption optimal allocation; an irreversible investement allocation problem.
Interst rate models: the risk premium. The CIR model.
Recommended Bibliography Pham, H.: Continuous-time Stochastic Control and Optimization with Financial Applications, Springer 2009
De Giuli, M.E., Maggi, M.A.,Magnani, U., Rossi, E.: Derivati. Teoria e applicazioni. Giappichelli 2002
Methods of Provision
Teaching Methods classroom-taught lessons where theoretical aspects of the discipline are investigated
and applied to concrete problems.
Evaluation methods Verification of learning:
The exam is oral. Questions will spring from some problems on which the students will have worked autonomously during the course.
Contacts/More Information Office hours:
- 2 hours per week with dates and times communicated at the beginning of the course;
- on request by reservation via e-mail.