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The cooperation and contamination among mathematicians, statisticians and econometricians working in actuarial sciences and finance are improving the research on these topics and producing numerous meaningful scientific results. This volume presents new ideas in the form of four- to six-page papers presented at the International Conference MAF2022 – Mathematical and Statistical Methods for Actuarial Sciences and Finance. Due to the COVID-19 pandemic, the conference, to which this book is related, was organized in a hybrid form by the Department of Economics and Statistics of the University of Salerno, with the partnership of the Department of Economics of Cà Foscari University of Venice, and was held from 20 to 22 April 2022 in Salerno (Italy) MAF2022 is the tenth edition of an international biennial series of scientific meetings, started in 2004 on the initiative of the Department of Economics and Statistics of the University of Salerno. It has establisheditself internationally with gradual and continuous growth and scientific enrichment. The effectiveness of this idea has been proven by the wide participation in all the editions, which have been held in Salerno (2004, 2006, 2010, 2014, 2022), Venice (2008, 2012 and 2020 online), Paris (2016) and Madrid (2018). This book covers a wide variety of subjects: artificial intelligence and machine learning in finance and insurance, behavioural finance, credit risk methods and models, dynamic optimization in finance, financial data analytics, forecasting dynamics of actuarial and financial phenomena, foreign exchange markets, insurance models, interest rate models, longevity risk, models and methods for financial time series analysis, multivariate techniques for financial markets analysis, pension systems, portfolio selection and management, real-world finance, risk analysis and management, trading systems, and others. This volume is a valuable resource for academics, PhD students, practitioners, professionals and researchers. Moreover, it is also of interest to other readers with quantitative background knowledge.

The cooperation and contamination between mathematicians, statisticians and econometricians working in actuarial sciences and finance is improving the research on these topics and producing numerous meaningful scientific results. This volume presents new ideas, in the form of four- to six-page papers, presented at the International Conference eMAF2020 – Mathematical and Statistical Methods for Actuarial Sciences and Finance. Due to the now sadly famous COVID-19 pandemic, the conference was held remotely through the Zoom platform offered by the Department of Economics of the Ca'Foscari University of Venice on September 18, 22 and 25, 2020. eMAF2020 is the ninth edition of an international biennial series of scientific meetings, started in 2004 at the initiative of the Department of Economics and Statistics of the University of Salerno. The effectiveness of this idea has been proven by wide participation in all editions, which have been held in Salerno (2004, 2006, 2010 and 2014), Venice (2008, 2012 and 2020), Paris (2016) and Madrid (2018). This book covers a wide variety of subjects: artificial intelligence and machine learning in finance and insurance, behavioral finance, credit risk methods and models, dynamic optimization in finance, financial data analytics, forecasting dynamics of actuarial and financial phenomena, foreign exchange markets, insurance models, interest rate models, longevity risk, models and methods for financial time series analysis, multivariate techniques for financial markets analysis, pension systems, portfolio selection and management, real-world finance, risk analysis and management, trading systems, and others. This volume is a valuable resource for academics, PhD students, practitioners, professionals and researchers. Moreover, it is also of interest to other readers with quantitative background knowledge.

The interaction between mathematicians, statisticians and econometricians working in actuarial sciences and finance is producing numerous meaningful scientific results. This volume introduces new ideas, in the form of four-page papers, presented at the international conference Mathematical and Statistical Methods for Actuarial Sciences and Finance (MAF), held at Universidad Carlos III de Madrid (Spain), 4th-6th April 2018. The book covers a wide variety of subjects in actuarial science and financial fields, all discussed in the context of the cooperation between the three quantitative approaches. The topics include: actuarial models; analysis of high frequency financial data; behavioural finance; carbon and green finance; credit risk methods and models; dynamic optimization in finance; financial econometrics; forecasting of dynamical actuarial and financial phenomena; fund performance evaluation; insurance portfolio risk analysis; interest rate models; longevity risk; machine learning and soft-computing in finance; management in insurance business; models and methods for financial time series analysis, models for financial derivatives; multivariate techniques for financial markets analysis; optimization in insurance; pricing; probability in actuarial sciences, insurance and finance; real world finance; risk management; solvency analysis; sovereign risk; static and dynamic portfolio selection and management; trading systems. This book is a valuable resource for academics, PhD students, practitioners, professionals and researchers, and is also of interest to other readers with quantitative background knowledge.

This book is divided into two parts, the first of which seeks to connect the phase transitions of various disciplines, including game theory, and to explore the synergies between statistical physics and combinatorics. Phase Transitions has been an active multidisciplinary field of research, bringing together physicists, computer scientists and mathematicians. The main research theme explores how atomic agents that act locally and microscopically lead to discontinuous macroscopic changes. Adopting this perspective has proven to be especially useful in studying the evolution of random and usually complex or large combinatorial objects (like networks or logic formulas) with respect to discontinuous changes in global parameters like connectivity, satisfiability etc. There is, of course, an obvious strategic element in the formation of a transition: the atomic agents “selfishly” seek to optimize a local parameter. However, up to now this game-theoretic aspect of abrupt, locallytriggered changes had not been extensively studied. In turn, the book's second part is devoted to mathematical and computational methods applied to the pricing of financial contracts and the measurement of financial risks. The tools and techniques used to tackle these problems cover a wide spectrum of fields, like stochastic calculus, numerical analysis, partial differential equations, statistics and econometrics. Quantitative Finance is a highly active field of research and is increasingly attracting the interest of academics and practitioners alike. The material presented addresses a wide variety of new challenges for this audience.

This volume gathers selected peer-reviewed papers presented at the international conference'MAF 2016 – Mathematical and Statistical Methods for Actuarial Sciences and Finance”, held in Paris (France) at the Université Paris-Dauphine from March 30 to April 1, 2016.The contributions highlight new ideas on mathematical and statistical methods in actuarial sciences and finance. The cooperation between mathematicians and statisticians working in insurance and finance is a very fruitful field, one that yields unique theoretical models and practical applications, as well as new insights in the discussion of problems of national and international interest. This volume is addressed to academicians, researchers, Ph.D. students and professionals.

These Proceedings offer a selection of peer-reviewed research and survey papers by some of the foremost international researchers in the fields of finance, energy, stochastics and risk, who present their latest findings on topical problems. The papers cover the areas of stochastic modeling in energy and financial markets; risk management with environmental factors from a stochastic control perspective; and valuation and hedging of derivatives in markets dominated by renewables, all of which further develop the theory of stochastic analysis and mathematical finance. The papers were presented at the first conference on “Stochastics of Environmental and Financial Economics (SEFE)”, being part of the activity in the SEFE research group of the Centre of Advanced Study (CAS) at the Academy of Sciences in Oslo, Norway during the 2014/2015 academic year.

The interaction between mathematicians and statisticians has been shown to be an effective approach for dealing with actuarial, insurance and financial problems, both from an academic perspective and from an operative one. The collection of original papers presented in this volume pursues precisely this purpose. It covers a wide variety of subjects in actuarial, insurance and finance fields, all treated in the light of the successful cooperation between the above two quantitative approaches. The papers published in this volume present theoretical and methodological contributions and their applications to real contexts. With respect to the theoretical and methodological contributions, some of the considered areas of investigation are: actuarial models; alternative testing approaches; behavioral finance; clustering techniques; coherent and non-coherent risk measures; credit scoring approaches; data envelopment analysis; dynamic stochastic programming; financial contagion models; financial ratios; intelligent financial trading systems; mixture normality approaches; Monte Carlo-based methods; multicriteria methods; nonlinear parameter estimation techniques; nonlinear threshold models; particle swarm optimization; performance measures; portfolio optimization; pricing methods for structured and non-structured derivatives; risk management; skewed distribution analysis; solvency analysis; stochastic actuarial valuation methods; variable selection models; time series analysis tools. As regards the applications, they are related to real problems associated, among the others, to: banks; collateralized fund obligations; credit portfolios; defined benefit pension plans; double-indexed pension annuities; efficient-market hypothesis; exchange markets; financial time series; firms; hedge funds; non-life insurance companies; returns distributions; socially responsible mutual funds; unit-linked contracts. This book is aimed at academics, Ph.D.students, practitioners, professionals and researchers. But it will also be of interest to readers with some quantitative background knowledge.

This volume aims to collect new ideas presented in the form of 4 page papers dedicated to mathematical and statistical methods in actuarial sciences and finance. The cooperation between mathematicians and statisticians working in insurance and finance is a very fruitful field and provides interesting scientific products in theoretical models and practical applications, as well as in scientific discussion of problems of national and international interest. This work reflects the results discussed at the biennial conference on Mathematical and Statistical Methods for Actuarial Sciences and Finance (MAF), born at the University of Salerno in 2004.

Advances in Stochastic Modelling and Data Analysis presents the most recent developments in the field, together with their applications, mainly in the areas of insurance, finance, forecasting and marketing. In addition, the possible interactions between data analysis, artificial intelligence, decision support systems and multicriteria analysis are examined by top researchers. Audience: A wide readership drawn from theoretical and applied mathematicians, such as operations researchers, management scientists, statisticians, computer scientists, bankers, marketing managers, forecasters, and scientific societies such as EURO and TIMS.

This volume contains selected papers that were presented at the International Conference COMPUTATIONAL FINANCE 1997 held at London Business School on December 15-17 1997. Formerly known as Neural Networks in the Capital Markets (NNCM), this series of meetings has emerged as a truly multi-disciplinary international conference and provided an international focus for innovative research on the application of a multiplicity of advanced decision technologies to many areas of financial engineering. It has drawn upon theoretical advances in financial economics and robust methodological developments in the statistical, econometric and computer sciences. To reflect its multi-disciplinary nature, the NNCM conference has adopted the new title COMPUTATIONAL FINANCE. The papers in this volume are organised in six parts. Market Dynamics and Risk, Trading and Arbitrage strategies, Volatility and Options, Term-Structure and Factor models, Corporate Distress Models and Advances on Methodology. This years'acceptance rate (38%) reflects both the increasing interest in the conference and the Programme Committee's efforts to improve the quality of the meeting year-on-year. I would like to thank the members of the programme committee for their efforts in refereeing the papers. I also would like to thank the members of the computational finance group at London Business School and particularly Neil Burgess, Peter Bolland, Yves Bentz, and Nevil Towers for organising the meeting.

The articles included in the volume cover a range of diverse topics linked by a common theme: the use of formal modelling techniques to promote better understanding of financial markets and improve management of financial operations.Apart from a theoretical discussion, most of the papers model validation or verification using market data. This collection of articles sets the framework for other studies that could link theory and practice.

This book contains a selection of the papers presented at the 24th Meeting of the Euro Working Group on Financial Modelling held in Valencia, Spain, on April 8-10, 1.999. The Meeting took place in the Bancaja Cultural Center, a nice palace of the XIX century, located in the center of the city. Traditionally, members of the Euro Working Group on Financial Mod­ elling meet twice a year, hosted by different active groups in successions. The year 1999 was very special for us because the University of Valencia celebrates its fifth century. The Meeting was very well attended and of high quality. More than 90 participants, coming from 20 different countries debated 46 communications in regular sessions. The opening lecture was given by Prof. H. White, from the University of California, San Diego. The topics discussed were classified in nine sessions: Financial Theory, Financial Time Series, Risk Analysis, Portfolio Analysis, Financial Institu­ tions, Microstructures Market and Corporate Finance, Methods in Finance, Models in Finance and Derivatives. The papers collected in this volume provide a representative but not com­ plete sample of the fields where the members of the working group develop their scientific activity. The papers are a sample of this activity, and consist of theoretical papers as well as empirical ones.

The book develops the capabilities arising from the cooperation between mathematicians and statisticians working in insurance and finance fields. It gathers some of the papers presented at the conference MAF2010, held in Ravello (Amalfi coast), and successively, after a reviewing process, worked out to this aim.

This volume is centered around the issue of market design and resulting market dynamics. The economic crisis of 2007-2009 has once again highlighted the importance of a proper design of market protocols and institutional details for economic dynamics and macroeconomics. Papers in this volume capture institutional details of particular markets, behavioral details of agents'decision making as well as spillovers between markets and effects to the macroeconomy. Computational methods are used to replicate and understand market dynamics emerging from interaction of heterogeneous agents, and to develop models that have predictive power for complex market dynamics. Finally treatments of overlapping generations models and differential games with heterogeneous actors are provided.

This book introduces some advanced topics in probability theories — both pure and applied — is divided into two parts. The first part deals with the analysis of stochastic dynamical systems, in terms of Gaussian processes, white noise theory, and diffusion processes. The second part of the book discusses some up-to-date applications of optimization theories, martingale measure theories, reliability theories, stochastic filtering theories and stochastic algorithms towards mathematical finance issues such as option pricing and hedging, bond market analysis, volatility studies and asset trading modeling.

The primary goal of the book is to present the ideas and research findings of active researchers from various communities (physicists, economists, mathematicians, financial engineers) working in the field of'Econophysics', who have undertaken the task of modelling and analyzing order-driven markets. Of primary interest in these studies are the mechanisms leading to the statistical regularities ('stylized facts') of price statistics. Results pertaining to other important issues such as market impact, the profitability of trading strategies, or mathematical models for microstructure effects, are also presented. Several leading researchers in these fields report on their recent work and also review the contemporary literature. Some historical perspectives, comments and debates on recent issues in Econophysics research are also included.

Featuring international contributors from both industry and academia, Numerical Methods for Finance explores new and relevant numerical methods for the solution of practical problems in finance. It is one of the few books entirely devoted to numerical methods as applied to the financial field.Presenting state-of-the-art methods in this area

The interaction between mathematicians and statisticians reveals to be an effective approach to the analysis of insurance and financial problems, in particular in an operative perspective. The Maf2006 conference, held at the University of Salerno in 2006, had precisely this purpose and the collection here published gathers some of the papers presented at the conference and successively worked out to this aim. They cover a wide variety of subjects in insurance and financial fields, all treated in light of the successful cooperation between the two quantitative methods.

Econophysicists have recently been quite successful in modelling and analysing various financial systems like trading, banking, stock and other markets. The statistical behaviour of the underlying networks in these systems have also been identified and characterised recently. This book reviews the current econophysics researches in the structure and functioning of these complex financial network systems. Leading researchers in the respective fields will report on their recent researches and review on the contemporary developments. The book will also include the comments and debates on the latest issues arising out of these

This self-contained volume brings together a collection of chapters by some of the most distinguished researchers and practitioners in the fields of mathematical finance and financial engineering. Presenting state-of-the-art developments in theory and practice, the Festschrift is dedicated to Dilip B. Madan on the occasion of his 60th birthday.Specific topics covered include:• Theory and application of the Variance-Gamma process• Lévy process driven fixed-income and credit-risk models, including CDO pricing• Numerical PDE and Monte Carlo methods• Asset pricing and derivatives valuation and hedging• Itô formulas for fractional Brownian motion• Martingale characterization of asset price bubbles• Utility valuation for credit derivatives and portfolio managementAdvances in Mathematical Finance is a valuable resource for graduate students, researchers, and practitioners in mathematical finance and financialengineering.Contributors: H. Albrecher, D. C. Brody, P. Carr, E. Eberlein, R. J. Elliott, M. C. Fu, H. Geman, M. Heidari, A. Hirsa, L. P. Hughston, R. A. Jarrow, X. Jin, W. Kluge, S. A. Ladoucette, A. Macrina, D. B. Madan, F. Milne, M. Musiela, P. Protter, W. Schoutens, E. Seneta, K. Shimbo, R. Sircar, J. van der Hoek, M.Yor, T. Zariphopoulou

This volume contains the contributions to a conference that is among the most important meetings in financial mathematics. Serving as a bridge between probabilists in Japan (called the Ito School and known for its highly sophisticated mathematics) and mathematical finance and financial engineering, the conference elicits the very highest quality papers in the field of financial mathematics.

Understanding the mechanism of a socio-economic system requires more than an understanding of the individuals that comprise the system. It also requires understanding how individuals interact with each other, and how the agg- gated outcome can be more than the sum of individual behaviors. This book contains the papers fostering the formation of an active multi-disciplinary community on socio-economic systems with the exciting new?elds of age- based modeling and econophysics. We especially intend to increase the awareness of researchers in many?elds with sharing the common view many economic and social activities as collectives of a large-scale heterogeneous and interacting agents. Economists seek to understand not only how individuals behave but also how the interaction of many individuals leads to complex outcomes. Age- based modeling is a method for studying socio-economic systems exhibiting the following two properties: (1) the system is composed of interacting agents, and (2) the system exhibits emergent properties, that is, properties arising from the interactions of the agents that cannot be deduced simply by agg- gating the properties of the system's components. When the interaction of the agents is contingent on past experience, and especially when the agents continually adapt to that experience, mathematical analysis is typically very limited in its ability to derive the outcome.

Some economic phenomena are predictable and controllable, and some are impos­ sible to foresee. Existing economic theories do not provide satisfactory answers as to what degree economic phenomena can be predicted and controlled, and in what situations. Against this background, people working on the financial front lines in real life have to rely on empirical rules based on experiments that often lack a solid foundation.'Econophysics'is a new science that analyzes economic phenomena empirically from a physical point of view, and it is being studied mainly to offer scientific, objective and significant answers to such problems. This book is the proceedings of the third Nikkei symposium on''Practical Fruits of Econophysics,'held in Tokyo, November 9-11, 2004. In the first symposium held in 2000, empirical rules were established by analyzing high-frequency finan­ cial data, and various kinds of theoretical approaches were confimied. In the second symposium, in 2002, the predictability of imperfections and of economic fluctua­ tions was discussed in detail, and methods for applying such studies were reported. The third symposium gave an overview of practical developments that can immedi­ ately be applied to the financial sector, or at least provide hints as to how to use the methodology.

Based around recent lectures given at the prestigious Ritsumeikan conference, the tutorial and expository articles contained in this volume are an essential guide for practitioners and graduates alike who use stochastic calculus in finance.Among the eminent contributors are Paul Malliavin and Shinzo Watanabe, pioneers of Malliavin Calculus. The coverage also includes a valuable review of current research on credit risks in a mathematically sophisticated way contrasting with existing economics-oriented articles.

This book reviews the latest econophysics researches on the fluctuations in stock, forex and other markets. The statistical modeling of markets, using various agent-based game theoretical approaches, and their scaling analysis have been discussed. The leading researchers in these fields have reported on their recent work and also reviewed the contemporary literature. Some historical perspectives as well as some comments and debates on recent issues in econophysics research have also been included.

We all know the hard fact: neither wealth nor income is ever uniform for us all. Justified or not, they are unevenly distributed; few are rich and many are poor! Investigations for more than hundred years and the recent availability of the income distribution data in the internet (made available by the finance ministries of various countries; from the tax return data of the income tax departments) have revealed some remarkable features. Irrespective of many differences in culture, history, language and, to some extent, the economic policies followed in different countries, the income distribution is seen to fol­ low a particular universal pattern. So does the wealth distribution. Barring an initial rise in population with income (or wealth; for the destitutes), the population decreases either exponentially or in a log-normal way for the ma­ jority of'middle income'group, and it eventually decreases following a power law (Pareto law, following Vilfredo Pareto's observation in 1896) for the rich­ est 5-10% of the population! This seems to be an universal feature - valid for most of the countries and civilizations; may be in ancient Egypt as well! Econophysicists tried to view this as a natural law for a statistical ma- body-dynamical market system, analogous to gases, liquids or solids: classical or quantum.

This book contains 17 articles on stochastic processes (stochastic calculus and Malliavin calculus, functionals of Brownian motions and Lévy processes, stochastic control and optimization problems, stochastic numerics, and so on) and their applications to problems in mathematical finance.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• Index to Social Sciences & Humanities Proceedings® (ISSHP® / ISI Proceedings)• Index to Social Sciences & Humanities Proceedings (ISSHP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences

This workshop was the first of its kind in bringing together researchers in probability theory, stochastic processes, insurance and finance from mainland China, Taiwan, Hong Kong, Singapore, Australia and the United States. In particular, as China has joined the WTO, there is a growing demand for expertise in actuarial sciences and quantitative finance. The strong probability research and graduate education programs in many of China's universities can be enriched by their outreach in fields that are of growing importance to the country's expanding economy, and the workshop and its proceedings can be regarded as the first step in this direction.This book presents the most recent developments in probability, finance and actuarial sciences, especially in Chinese probability research. It focuses on the integration of probability theory with applications in finance and insurance. It also brings together academic researchers and those in industry and government. With contributions by leading authorities on probability theory — particularly limit theory and large derivations, valuation of credit derivatives, portfolio selection, dynamic protection and ruin theory — it is an essential source of ideas and information for graduate students and researchers in probability theory, mathematical finance and actuarial sciences, and thus every university should acquire a copy.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• Index to Social Sciences & Humanities Proceedings® (ISSHP® / ISI Proceedings)• Index to Social Sciences & Humanities Proceedings (ISSHP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences

Econophysics is a newborn field of science bridging economics and physics. A special feature of this new science is the data analysis of high-precision market data. In economics arbitrage opportunity is strictly denied; however, by observing high-precision data we can prove the existence of arbitrage opportunity. Also, financial technology neglects the possibility of market prediction; however, in this book you can find many examples of predicted events. There are other surprising findings. This volume is the proceedings of a workshop on'application of econophysics'at which leading international researchers discussed their most recent results.

Financial fluctuations were generally neglected in classical ecnomics and their basic statistical properties have only recently been elucidated in the emerging field of econophysics, a new science that analyzes data using methods developed by statistical physics, such as chaos, fractals, and phase transitions. This volume is the proceedings of a workshop at which leading international researchers in this discipline discussed their most recent results and examined the validity of the empirical laws of econophysics. Topics include stock market prices and foreign exchange rates, income distribution, market anomalies, and risk management. The papers herein relate econophysics to other models, present new models, and illustrate the mechanisms by which financial fluctuations occur using actual financial data. Containing the most recent econophysics results, this volume will serve as an indispensable reference for economic theorists and practitioners alike.

This invaluable book contains lectures presented at the Courant Institute's Mathematical Finance Seminar. The audience consisted of academics from New York University and other universities, as well as practitioners from investment banks, hedge funds and asset-management firms.

This book contains lectures delivered at the celebrated Seminar in Mathematical Finance at the Courant Institute. The lecturers and presenters of papers are prominent researchers and practitioners in the field of quantitative financial modeling. Most are faculty members at leading universities or Wall Street practitioners.The lectures deal with the emerging science of pricing and hedging derivative securities and, more generally, managing financial risk. Specific articles concern topics such as option theory, dynamic hedging, interest-rate modeling, portfolio theory, price forecasting using statistical methods, etc.

This book covers the techniques of data mining, knowledge discovery, genetic algorithms, neural networks, bootstrapping, machine learning, and Monte Carlo simulation.Computational finance, an exciting new cross-disciplinary research area, draws extensively on the tools and techniques of computer science, statistics, information systems, and financial economics. This book covers the techniques of data mining, knowledge discovery, genetic algorithms, neural networks, bootstrapping, machine learning, and Monte Carlo simulation. These methods are applied to a wide range of problems in finance, including risk management, asset allocation, style analysis, dynamic trading and hedging, forecasting, and option pricing. The book is based on the sixth annual international conference Computational Finance 1999, held at New York University's Stern School of Business.

This invaluable book contains lectures delivered at the celebrated Seminar in Mathematical Finance at the Courant Institute. The lecturers and presenters of papers are prominent researchers and practitioners in the field of quantitative financial modeling. Most are faculty members at leading universities or Wall Street practitioners.The lectures deal with the emerging science of pricing and hedging derivative securities and, more generally, managing financial risk. Specific articles concern topics such as option theory, dynamic hedging, interest-rate modeling, portfolio theory, price forecasting using statistical methods, etc.

The analysis prediction and interpolation of economic and other time series has a long history and many applications. Major new developments are taking place, driven partly by the need to analyze financial data. The five papers in this book describe those new developments from various viewpoints and are intended to be an introduction accessible to readers from a range of backgrounds.The book arises out of the second Seminaire European de Statistique (SEMSTAT) held in Oxford in December 1994. This brought together young statisticians from across Europe, and a series of introductory lectures were given on topics at the forefront of current research activity. The lectures form the basis for the five papers contained in the book.The papers by Shephard and Johansen deal respectively with time series models for volatility, i.e. variance heterogeneity, and with cointegration. Clements and Hendry analyze the nature of prediction errors. A complementary review paper by Laird gives a biometrical view of the analysis of short time series. Finally Astrup and Nielsen give a mathematical introduction to the study of option pricing. Whilst the book draws its primary motivation from financial series and from multivariate econometric modelling, the applications are potentially much broader.