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Financial Mathematics: From Discrete to Continuous Time is a study of the mathematical ideas and techniques that are important to the two main arms of the area of financial mathematics: portfolio optimization and derivative valuation. The text is authored for courses taken by advanced undergraduates, MBA, or other students in quantitative finance programs. The approach will be mathematically correct but informal, sometimes omitting proofs of the more difficult results and stressing practical results and interpretation. The text will not be dependent on any particular technology, but it will be laced with examples requiring the numerical and graphical power of the machine. The text illustrates simulation techniques to stand in for analytical techniques when the latter are impractical. There will be an electronic version of the text that integrates Mathematica functionality into the development, making full use of the computational and simulation tools that this program provides. Prerequisites are good courses in mathematical probability, acquaintance with statistical estimation, and a grounding in matrix algebra. The highlights of the text are: A thorough presentation of the problem of portfolio optimization, leading in a natural way to the Capital Market Theory Dynamic programming and the optimal portfolio selection-consumption problem through time An intuitive approach to Brownian motion and stochastic integral models for continuous time problems The Black-Scholes equation for simple European option values, derived in several different ways A chapter on several types of exotic options Material on the management of risk in several contexts
Topics include managing checking and savings accounts, understanding credit cards and loans, owning a home, investing, and paying taxes.
Versatile for Several Interrelated Courses at the Undergraduate and Graduate Levels Financial Mathematics: A Comprehensive Treatment provides a unified, self-contained account of the main theory and application of methods behind modern-day financial mathematics. Tested and refined through years of the authors’ teaching experiences, the book encompasses a breadth of topics, from introductory to more advanced ones. Accessible to undergraduate students in mathematics, finance, actuarial science, economics, and related quantitative areas, much of the text covers essential material for core curriculum courses on financial mathematics. Some of the more advanced topics, such as formal derivative pricing theory, stochastic calculus, Monte Carlo simulation, and numerical methods, can be used in courses at the graduate level. Researchers and practitioners in quantitative finance will also benefit from the combination of analytical and numerical methods for solving various derivative pricing problems. With an abundance of examples, problems, and fully worked out solutions, the text introduces the financial theory and relevant mathematical methods in a mathematically rigorous yet engaging way. Unlike similar texts in the field, this one presents multiple problem-solving approaches, linking related comprehensive techniques for pricing different types of financial derivatives. The book provides complete coverage of both discrete- and continuous-time financial models that form the cornerstones of financial derivative pricing theory. It also presents a self-contained introduction to stochastic calculus and martingale theory, which are key fundamental elements in quantitative finance.
This volume is an excellent resource for professionals in various areas of applications of mathematics, modeling, and computational science. It focuses on recent progress and modern challenges in these areas. The volume provides a balance between fundamental theoretical and applied developments, emphasizing the interdisciplinary nature of modern trends and detailing state-of-the-art achievements in Applied Mathematics, Modeling, and Computational Science. The chapters have been authored by international experts in their respective fields, making this book ideal for researchers in academia, practitioners, and graduate students. It can also serve as a reference in the diverse selected areas of applied mathematics, modelling, and computational sciences, and is ideal for interdisciplinary collaborations.
This book contains high-quality papers presented at the First International Forum on Financial Mathematics and Financial Technology. With the rapid development of FinTech, the in-depth integration between mathematics, finance and advanced technology is the general trend. This book focuses on selected aspects of the current and upcoming trends in FinTech. In detail, the included scientific papers focus on financial mathematics and FinTech, presenting the innovative mathematical models and state-of-the-art technologies such as deep learning, with the aim to improve our financial analysis and decision-making and enhance the quality of financial services and risk control. The variety of the papers delivers added value for both scholars and practitioners where they will find perfect integration of elegant mathematical models and up-to-date data mining technologies in financial market analysis.
Blending the topics of both accounting and finance, Essentials of Health Care Finance is a relevant, readable, and easily applied resource for health care management students and executives that explores finance theory and its practical application in health care across a full range of facilities, from hospitals, home health agencies, and skilled nursing facilities to surgical centers, physician practices, and integrated health systems. Carefully revised, the Ninth Edition of Essentials of Health Care Finance has been updated with additional reflection, examples, and application so that individuals with no healthcare experience can benefit from additional elaboration on key concepts such as physician practice management, flex budgeting, and strategic financial planning. The Ninth Edition also explores trends in national health expenditures and physician organizations and alignment; changes in health services financing and utilization since the enactment of the Affordable Care Act (ACA)
Essentials of Health Care Finance stands firmly in its place as the leading textbook on healthcare finance. No other text so completely blends the best of current finance theory with the tools needed in day-to-day practice. Useful for all course levels as well as a professional reference, this text offers a comprehensive introduction to the field. The Seventh Edition has been thoroughly revised to reflect the current economic environment in the healthcare industry, with thoughtful descriptions and ‘real-world’ examples. As the not-for-profit health care sector has increasingly come under attack by legislators seeking new sources of tax revenue, this edition also features a new chapter on assessing community benefits including an examination of the new Schedule H of the IRS 990 form. Ancillary instructor materials for the Seventh Edition have been significantly expanded and updated. PowerPoint lecture slides now include selected examples from the chapters. Electronic versions of many of the charts and tables in the chapters are provided to enable the instructor to re-create and modify existing examples. An expanded set of test questions with detailed answers will be provided for each chapter. New excel spreadsheets for selected chapters will be created to help both the students and the instructors perform a variety of financial analysis tasks with spreadsheet templates. The instructor’s manual has been revised to include key learning points, chapter overviews, and guidelines for class discussion.