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Mathematical models in the social sciences have become increasingly sophisticated and widespread in the last decade. This period has also seen many critiques, most lamenting the sacrifices incurred in pursuit of mathematical rigor. If, as critics argue, our ability to understand the world has not improved during the mathematization of the social sciences, we might want to adopt a different paradigm. This book examines the three main fields of mathematical modeling - game theory, statistics, and computational methods - and proposes a new framework for modeling. Unlike previous treatments which view each field separately, the treatment provides a framework that spans and incorporates the different methodological approaches. The goal is to arrive at a new vision of modeling that allows researchers to solve more complex problems in the social sciences. Additionally, a special emphasis is placed upon the role of computational modeling in the social sciences.
Social sciences --- Sciences sociales --- Mathematical models. --- Modèles mathématiques --- Social Sciences --- Political Science
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Knowledge of risk models and the assessment of risk is a fundamental part of the training of actuaries and all who are involved in financial, pensions and insurance mathematics. This book provides students and others with a firm foundation in a wide range of statistical and probabilistic methods for the modelling of risk, including short-term risk modelling, model-based pricing, risk-sharing, ruin theory and credibility. It covers much of the international syllabuses for professional actuarial examinations in risk models, but goes into further depth, with worked examples, exercises and detailed case studies. The authors also use the statistical package R to demonstrate how simple code and functions can be used profitably in an actuarial context. The authors' engaging and pragmatic approach, balancing rigour and intuition and developed over many years of teaching the subject, makes this book ideal for self-study or for students taking courses in risk modelling.
Risk (Insurance) --- Risque (Assurance) --- Mathematical models. --- Modèles mathématiques --- Mathematics --- Applied. --- Modèles mathématiques --- Insurance --- Business mathematics --- Actuarial science --- Mathematics.
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Finance --- Risk management --- Finances --- Gestion du risque --- Mathematical models --- Modèles mathématiques --- Modèles mathématiques --- Insurance --- Management
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This book presents a model which simulates the effects of financial reforms in transitional economies, which is then applied to Poland for a variety of policy simulations. The authors develop models for households, commercial banks and firms, expanding their enquiry into the government sector, the central banking sector, the external sector and finally the supply side. These sub-sector models explicitly incorporate institutional features specific to the Polish economy. The estimated model is used to simulate the effects of a wide array of financial policies introduced in Poland, and these resu
Finance --- Finances --- Mathematical models --- Modèles mathématiques --- Mathematical models. --- Modèles mathématiques --- Funding --- Funds --- Economics --- Currency question
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Polymers --- Mathematical models --- Periodicals. --- Data processing --- Polymères --- Modèles mathématiques --- Informatique --- Polymere --- Polymeride --- Polymers and polymerization --- Macromolecules
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The Black-Scholes option pricing model is the first and by far the best-known continuous-time mathematical model used in mathematical finance. Here, it provides a sufficiently complex, yet tractable, testbed for exploring the basic methodology of option pricing. The discussion of extended markets, the careful attention paid to the requirements for admissible trading strategies, the development of pricing formulae for many widely traded instruments and the additional complications offered by multi-stock models will appeal to a wide class of instructors. Students, practitioners and researchers alike will benefit from the book's rigorous, but unfussy, approach to technical issues. It highlights potential pitfalls, gives clear motivation for results and techniques and includes carefully chosen examples and exercises, all of which make it suitable for self-study.
Options (Finance) --- Options (Finances) --- Prices --- Mathematical models --- Prix --- Modèles mathématiques --- Mathematical Sciences --- Probability --- Investments --- Mathematical models.
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Authored by leading experts, this seminal text presents a straightforward and elementary account of coalescent theory, which is a central concept in the study of genetic sequence variation observed in a population. Rich in examples and illustrations it is ideal for a graduate course in statistics, population, molecular and medical genetics, bioscience and medicine, and for students studying the evolution of human population and disease.
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Stellar dynamics is an interdisciplinary field where mathematics, statistics, physics, and astronomy overlap. The approaches to studying a stellar system include dealing with the collisionless Boltzmann equation, the Chandrasekhar equations, and stellar hydrodynamic equations, which are comparable to the equations of motion of a compressible viscous fluid. Their equivalence gives rise to the closure problem, connected with the higher-order moments of the stellar velocity distribution, which is explained and solved for maximum entropy distributions and for any velocity distribution function, depending on a polynomial function in the velocity variables. On the other hand, the Milky Way kinematics in the solar neighbourhood needs to be described as a mixture distribution accounting for the stellar populations composing the Galactic components. As such, the book offers a statistical study, according to the moments and cumulants of a population mixture, and a dynamical approach, according to a superposition of Chandrasekhar stellar systems, connected with the potential function and the symmetries of the model.
Galactic dynamics. --- Stellar dynamics. --- Computer simulation. --- Mathematical models. --- Dynamique stellaire. --- Simulation par ordinateur. --- Modèles mathématiques.
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Mathematical modeling is the art and craft of building a system of equations that is both sufficiently complex to do justice to physical reality and sufficiently simple to give real insight into the situation. Mathematical Modeling: A Chemical Engineer's Perspective provides an elementary introduction to the craft by one of the century's most distinguished practitioners.Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author's frequently cited papers are reprint
Chemical engineering --- Mathematical models. --- Models, Mathematical --- Simulation methods --- Chemistry, Industrial --- Engineering, Chemical --- Industrial chemistry --- Engineering --- Chemistry, Technical --- Metallurgy --- Modèles mathématiques --- Modèles mathématiques --- Equations differentielles
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