Abstract :
[en] This doctoral dissertation in management science, entitled “Modelling Financial Data and
Portfolio Optimization Problems”, consists of two independent parts, whose unifying theme
is the construction and solution of mathematical programming models motivated by portfolio
selection problems. As such, this work is located at the interface of operations research and of
finance. It draws heavily on techniques and theoretical results originating in both disciplines.
The first part of the dissertation (Chapter 2) deals with an extension of Markowitz
model and takes into account some of the side-constraints faced by a decision-maker when
composing an investment portfolio, viz. lower and upper bounds on the quantities traded,
and upper bounds on the number of assets included in the portfolio. We focus on the
algorithmic difficulties raised by this model and we describe an original simulated annealing
heuristic for its solution.
The second (and largest) part of the thesis deals with a new multiperiod model for the
optimization of a portfolio of options linked to a single index (Chapters 4-10). The objective
of the model is to maximize the expected return of the portfolio under constraints limiting its
value-at-risk. The model contains several interesting features, like the possibility to rebalance
the portfolio with options introduced at the start of each period, explicit consideration of
transaction costs, realistic pricing of options, consideration of advanced probability models
to represent the future, etc. Some deep theoretical results from the financial literature
are exploited in order to enrich the model and to extend its applicability. In particular,
several available schemes for the generation of scenarios and for option pricing have been
critically examined, and the most appropriate ones have been implemented. Furthermore,
several optimization approaches (heuristic or exact procedures) have also been developed,
implemented and tested.
The models investigated in the dissertation bear on very different portfolio problems, draw
on separate streams of scientific literature, and are handled by distinct algorithmic techniques.
Therefore, the corresponding parts of the dissertation are fully independent, and each part
contains its own specific introduction and literature review.
