This book offers an introduction to the mathematical, probabilistic and numerical methods used in the modern theory of option pricing. The text is designed for readers with a basic mathematical background. The first part contains a presentation of the arbitrage theory in discrete time. In the second part, the theories of stochastic calculus and parabolic PDEs are developed in detail and the classical arbitrage theory is analyzed in a Markovian setting by means of of PDEs techniques. After the martingale representation theorems and the Girsanov theory have been presented, arbitrage pricing is revisited in the martingale theory optics. General tools from PDE and martingale theories are also used in the analysis of volatility modeling. The book also contains an Introduction to Lévy processes and Malliavin calculus. The last part is devoted to the description of the numerical methods used in option pricing: Monte Carlo, binomial trees, finite differences and Fourier transform.
With the Bologna Accords a bachelor-master-doctor curriculum has been introduced in various countries with the intention that students may enter the job market already at the bachelor level. Since financial Institutions provide non negligible job opportunities also for mathematicians, and scientists in general, it appeared to be appropriate to have a financial mathematics course already at the bachelor level in mathematics. Most mathematical techniques in use in financial mathematics are related to continuous time models and require thus notions from stochastic analysis that bachelor students do in general not possess. Basic notions and methodologies in use in financial mathematics can however be transmitted to students also without the technicalities from stochastic analysis by using discrete time (multi-period) models for which general notions from Probability suffice and these are generally familiar to students not only from science courses, but also from economics with quantitative curricula. There do not exists many textbooks for multi-period models and the present volume is intended to fill in this gap. It deals with the basic topics in financial mathematics and, for each topic, there is a theoretical section and a problem section. The latter includes a great variety of possible problems with complete solution.
This book is an introduction to mathematical biology for students with no experience in biology, but who have some mathematical background. The work is focused on population dynamics and ecology, following a tradition that goes back to Lotka and Volterra, and includes a part devoted to the spread of infectious diseases, a field where mathematical modeling is extremely popular. These themes are used as the area where to understand different types of mathematical modeling and the possible meaning of qualitative agreement of modeling with data. The book also includes a collections of problems designed to approach more advanced questions. This material has been used in the courses at the University of Trento, directed at students in their fourth year of studies in Mathematics. It can also be used as a reference as it provides up-to-date developments in several areas.
The date of the Eclogues is much debated.* A preliminary distinction is in order: that between the composition of the individual poems (which, at least in certain cases, were doubtless read immediately and circulated within a restricted group around the poet) and the publication of the final collection. There are only two obvious clues to the dating of the book: the land confiscations in the territory of Cremona and Mantua, which peaked in the aftermath of the battle of Philippi (though continuing during the early 30s BCE: cf. E. 1 and 9), and the consulship of Asinius Pollio, in 40 BCE (E. 4)"--
Internationalization is an essential component of the business model for luxury fashion companies. Hence, regardless of their size, luxury firms have to develop in foreign markets to seek global demand, build a global image, and manage distribution and communications effectively. Filling a gap in current literature, this book examines the motives, processes, and forms assumed for the internationalization of luxury fashion companies and the relationship between internationalization and business models, with a focus on small and medium-sized enterprises (SMEs) and the specific challenges they face. The book proposes cases of Italian SMEs, being Italy a country that is globally recognized as a key player in the luxury fashion industry. Specifically, the authors link internationalization with business models and discuss the business model of luxury fashion SMEs, characterized by "genetic internationalization". Finally, the authors address the main theoretical and managerial implications emerging from their empirical research and discuss the applicability of this model to luxury companies in general. Offering a comprehensive and in-depth view of luxury fashion SMEs, this book is targeted to students, scholars and practitioners interested in luxury firms, internationalization, and business models.
This textbook offers a unique compendium of measurement procedures for experimental data acquisition. After introducing readers to the basic theory of uncertainty evaluation in measurements, it shows how to apply it in practice to conduct a range of laboratory experiments with instruments and procedures operating both in the time and frequency domains. Offering extensive practical information and hands-on tips on using oscilloscopes, spectrum analyzers and reflectometric instrumentation, the book shows readers how to deal with e.g. filter characterization, operational amplifiers, digital and analogic spectral analysis, and reflectometry-based measurements. For each experiment, it describes the corresponding uncertainty evaluation in detail. Bridging the gap between theory and practice, the book offers a unique, self-contained guide for engineering students and professionals alike. It also provides university teachers and professors with a valuable resource for their laboratory courses on electric and electronic measurements.
This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is accessible to graduate students and requires no specialized knowledge in algebra or differential geometry.
This book offers an introduction to the mathematical, probabilistic and numerical methods used in the modern theory of option pricing. The text is designed for readers with a basic mathematical background. The first part contains a presentation of the arbitrage theory in discrete time. In the second part, the theories of stochastic calculus and parabolic PDEs are developed in detail and the classical arbitrage theory is analyzed in a Markovian setting by means of of PDEs techniques. After the martingale representation theorems and the Girsanov theory have been presented, arbitrage pricing is revisited in the martingale theory optics. General tools from PDE and martingale theories are also used in the analysis of volatility modeling. The book also contains an Introduction to Lévy processes and Malliavin calculus. The last part is devoted to the description of the numerical methods used in option pricing: Monte Carlo, binomial trees, finite differences and Fourier transform.
With the Bologna Accords a bachelor-master-doctor curriculum has been introduced in various countries with the intention that students may enter the job market already at the bachelor level. Since financial Institutions provide non negligible job opportunities also for mathematicians, and scientists in general, it appeared to be appropriate to have a financial mathematics course already at the bachelor level in mathematics. Most mathematical techniques in use in financial mathematics are related to continuous time models and require thus notions from stochastic analysis that bachelor students do in general not possess. Basic notions and methodologies in use in financial mathematics can however be transmitted to students also without the technicalities from stochastic analysis by using discrete time (multi-period) models for which general notions from Probability suffice and these are generally familiar to students not only from science courses, but also from economics with quantitative curricula. There do not exists many textbooks for multi-period models and the present volume is intended to fill in this gap. It deals with the basic topics in financial mathematics and, for each topic, there is a theoretical section and a problem section. The latter includes a great variety of possible problems with complete solution.
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