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The Mathematics of Arbitrage
  • Language: en
  • Pages: 371

The Mathematics of Arbitrage

Proof of the "Fundamental Theorem of Asset Pricing" in its general form by Delbaen and Schachermayer was a milestone in the history of modern mathematical finance and now forms the cornerstone of this book. Puts into book format a series of major results due mostly to the authors of this book. Embeds highest-level research results into a treatment amenable to graduate students, with introductory, explanatory background. Awaited in the quantitative finance community.

Portfolio Theory and Arbitrage: A Course in Mathematical Finance
  • Language: en
  • Pages: 309

Portfolio Theory and Arbitrage: A Course in Mathematical Finance

This book develops a mathematical theory for finance, based on a simple and intuitive absence-of-arbitrage principle. This posits that it should not be possible to fund a non-trivial liability, starting with initial capital arbitrarily near zero. The principle is easy-to-test in specific models, as it is described in terms of the underlying market characteristics; it is shown to be equivalent to the existence of the so-called “Kelly” or growth-optimal portfolio, of the log-optimal portfolio, and of appropriate local martingale deflators. The resulting theory is powerful enough to treat in great generality the fundamental questions of hedging, valuation, and portfolio optimization. The bo...

Introduction to Mathematical Finance
  • Language: en
  • Pages: 184

Introduction to Mathematical Finance

The foundation for the subject of mathematical finance was laid nearly 100 years ago by Bachelier in his fundamental work, Theorie de la speculation. In this work, he provided the first treatment of Brownian motion. Since then, the research of Markowitz, and then of Black, Merton, Scholes, and Samuelson brought remarkable and important strides in the field. A few years later, Harrison and Kreps demonstrated the fundamental role of martingales and stochastic analysis in constructing and understanding models for financial markets. The connection opened the door for a flood of mathematical developments and growth. Concurrently with these mathematical advances, markets have grown, and developmen...

Optimality and Risk - Modern Trends in Mathematical Finance
  • Language: en
  • Pages: 281

Optimality and Risk - Modern Trends in Mathematical Finance

Problems of stochastic optimization and various mathematical aspects of risk are the main themes of this contributed volume. The readers learn about the recent results and techniques of optimal investment, risk measures and derivative pricing. There are also papers touching upon credit risk, martingale theory and limit theorems. Forefront researchers in probability and financial mathematics have contributed to this volume paying tribute to Yuri Kabanov, an eminent researcher in probability and mathematical finance, on the occasion of his 60th birthday. The volume gives a fair overview of these topics and the current approaches.

Advances in Finance and Stochastics
  • Language: en
  • Pages: 325

Advances in Finance and Stochastics

In many areas of finance and stochastics, significant advances have been made since this field of research was opened by Black, Scholes and Merton in 1973. This volume contains a collection of original articles by a number of highly distinguished authors, on research topics that are currently in the focus of interest of both academics and practitioners.

Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs
  • Language: en
  • Pages: 112

Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs

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Distributional Reinforcement Learning
  • Language: en
  • Pages: 385

Distributional Reinforcement Learning

  • Type: Book
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  • Published: 2023-05-30
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  • Publisher: MIT Press

The first comprehensive guide to distributional reinforcement learning, providing a new mathematical formalism for thinking about decisions from a probabilistic perspective. Distributional reinforcement learning is a new mathematical formalism for thinking about decisions. Going beyond the common approach to reinforcement learning and expected values, it focuses on the total reward or return obtained as a consequence of an agent's choices—specifically, how this return behaves from a probabilistic perspective. In this first comprehensive guide to distributional reinforcement learning, Marc G. Bellemare, Will Dabney, and Mark Rowland, who spearheaded development of the field, present its key...

In the Footsteps of Giorgio Philip Szegö
  • Language: en
  • Pages: 244

In the Footsteps of Giorgio Philip Szegö

This book offers essential information on the life and career of the recently deceased Giorgio P. Szegö, particularly his important contributions in various areas of mathematical programming and applications to financial markets. It highlights the developments in the fields of stability theory and dynamical systems brought about by his work in the early 1960s and 1970s, then moves on to address his valuable contributions to portfolio theory in the late 1970s and early 1980s, and, finally, examines his work in the field of risk management and the role of financial regulation in the late 1990s. The book explores Giorgio P. Szegö’s contributions in diverse research areas ranging from global optimization, theory of stability and dynamical systems to applications of financial mathematics to portfolio theory, risk measurement and financial regulation. It also covers his consulting work for such major international institutions as the IMF, World Bank and OECD.

Risk Management
  • Language: en
  • Pages: 790

Risk Management

Key readings in risk management from CFA Institute, the preeminent organization representing financial analysts Risk management may have been the single most important topic in finance over the past two decades. To appreciate its complexity, one must understand the art as well as the science behind it. Risk Management: Foundations for a Changing Financial World provides investment professionals with a solid framework for understanding the theory, philosophy, and development of the practice of risk management by Outlining the evolution of risk management and how the discipline has adapted to address the future of managing risk Covering the full range of risk management issues, including firm,...

Capital Markets, Fifth Edition
  • Language: en
  • Pages: 1087

Capital Markets, Fifth Edition

  • Type: Book
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  • Published: 2015-10-23
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  • Publisher: MIT Press

The substantially revised fifth edition of a textbook covering the wide range of instruments available in financial markets, with a new emphasis on risk management. Over the last fifty years, an extensive array of instruments for financing, investing, and controlling risk has become available in financial markets, with demand for these innovations driven by the needs of investors and borrowers. The recent financial crisis offered painful lessons on the consequences of ignoring the risks associated with new financial products and strategies. This substantially revised fifth edition of a widely used text covers financial product innovation with a new emphasis on risk management and regulatory ...