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This book on counting statistics presents a novel copula-based
approach to counting dependent random events. It combines
clustering, combinatorics-based algorithms and dependence structure
in order to tackle and simplify complex problems, without
disregarding the hierarchy of or interconnections between the
relevant variables. These problems typically arise in real-world
applications and computations involving big data in finance,
insurance and banking, where experts are confronted with counting
variables in monitoring random events. In this new approach,
combinatorial distributions of random events are the core element.
In order to deal with the high-dimensional features of the problem,
the combinatorial techniques are used together with a clustering
approach, where groups of variables sharing common characteristics
and similarities are identified and the dependence structure within
groups is taken into account. The original problems can then be
modeled using new classes of copulas, referred to here as
clusterized copulas, which are essentially based on preliminary
groupings of variables depending on suitable characteristics and
hierarchical aspects. The book includes examples and real-world
data applications, with a special focus on financial applications,
where the new algorithms' performance is compared to alternative
approaches and further analyzed. Given its scope, the book will be
of interest to master students, PhD students and researchers whose
work involves or can benefit from the innovative methodologies put
forward here. It will also stimulate the empirical use of new
approaches among professionals and practitioners in finance,
insurance and banking.
This book on counting statistics presents a novel copula-based
approach to counting dependent random events. It combines
clustering, combinatorics-based algorithms and dependence structure
in order to tackle and simplify complex problems, without
disregarding the hierarchy of or interconnections between the
relevant variables. These problems typically arise in real-world
applications and computations involving big data in finance,
insurance and banking, where experts are confronted with counting
variables in monitoring random events. In this new approach,
combinatorial distributions of random events are the core element.
In order to deal with the high-dimensional features of the problem,
the combinatorial techniques are used together with a clustering
approach, where groups of variables sharing common characteristics
and similarities are identified and the dependence structure within
groups is taken into account. The original problems can then be
modeled using new classes of copulas, referred to here as
clusterized copulas, which are essentially based on preliminary
groupings of variables depending on suitable characteristics and
hierarchical aspects. The book includes examples and real-world
data applications, with a special focus on financial applications,
where the new algorithms' performance is compared to alternative
approaches and further analyzed. Given its scope, the book will be
of interest to master students, PhD students and researchers whose
work involves or can benefit from the innovative methodologies put
forward here. It will also stimulate the empirical use of new
approaches among professionals and practitioners in finance,
insurance and banking.
True to its title, this book is focused on mathematical finance
field and it is draft in order to accomplish the level aimed at
second or third year undergraduate students, not only of
mathematics but also, for example, business management, finance and
economics. The aim of this book is to provide the basic concepts
concerning the mathematical finance which is unescapable to
understand the way modern financial markets operate.Thanks to these
fundamental concepts, which are completely concentrated on a
deterministic modelization of the markets, students are ready to
approach more advanced courses focused on the modern area of
financial math. Here the deterministic assumption is left and
stochastic assumptions concerning the evolution of the involved
variables are included.
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