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This accessible introduction to the mathematical underpinnings of finance concentrates on the probabilistic theory of continuous arbitrage pricing of financial derivatives. It includes a solved example for every new technique presented, numerous exercises, and a Further Reading list in each chapter.

Melvin Lax was a member of the US National Academy of Sciences, and widely known for his contributions in the field of random processes in physics. This book uniquely presents Lax's theoretical treatment of random processes, including applications to laser and semiconductor physics, light propagation in scattering media, and investment decisions.

Many different systems both in nature and in technology can be described by means of networks of interconnected components. Despite their different aspects, all of them share similar mathematical properties. In this book we explain how to recognize these features and why these different systems develop this common structure.

The Minority Game, invented in the late 1990s, makes it possible to understand stock market fluctuations in terms of information ecology between traders. With a minimal set of ingredients and drastic assumptions, this model reproduces market ecology among different types of traders. Its emphasis is on speculative trading and information flow.

Covering the pricing of assets, derivatives, and bonds in a discrete time, complete markets framework, this book is aimed at Masters and PhD students in finance. The topics covered include CAPM, non-marketable background risks, European style contingent claims as in Black-Scholes, and multi-period asset pricing under rational expectations.

Suitable for researchers and students in physics, mathematics and economics, as well as financial practitioners, this text describes the mathematical theory of Minority Games from a statistical mechanics viewpoint. It also provides a detailed introduction to the advanced mathematical analysis of these models.

This book takes a fresh look at understanding how financial markets behave. Using recent ideas from the highly-topical science of complexity and complex systems, the book provides the basis for a unified theoretical description of how today's markets really work. Since financial markets are an excellent example of a complex system, the book also doubles as a science textbook.

A collection of papers, accompanied by extensive discussion and commentary, by leading workers in credit scoring, this text focuses on recent developments and advances in this important area.