Mortgage Backed Securities (MBS) are among the most complex of all financial instruments. Analysis of MBS requires blending empirical analysis of borrower behavior with mathematical modeling of interest rates and home prices. Over the past 25 years, Davidson and Levin have been at the leading edge of MBS valuation and risk analysis. Mortgage Valuation Models: Embedded Options, Risk and Uncertainty is a detailed description of the sophisticated theories and advanced methods that the authors employ in real-world analysis of mortgage backed securities. Issues such as complexity, borrower options, uncertainty, and model risk play a central role in their approach to valuation of MBS. The book describes methods for modeling prepayments and defaults of borrowers. It explores closed form, backward induction and Monte Carlo valuation using the Option-Adjusted-Spread (OAS) approach, explains the origin of OAS and its relationship to model uncertainty. With reference to the classical CAPM and APT, the book advocates extending the concept of risk-neutrality to modeling home prices and borrower options, well beyond interest rates. The coverage spans the range of mortgage products from loans, TBA (to be announced) pass-through securities to subordinate tranches of subprime-mortgage securitizations and describes valuation methods for both agency and non-agency MBS including pricing new loans; Davidson and Levin put forth new approaches to prudent risk measurement, ranking, and decomposition that can help guide traders and risk managers. It reveals quantitative causes of the 2007-09 financial crisis and provides insights into the future of the US housing finance system and mortgage modeling. Despite the advances in mortgage modeling and valuation, this remains an ever-evolving field. Mortgage Valuation Models will serve as a foundation for the future development of models for mortgage-backed securities.

Difference algebra grew out of the study of algebraic difference equations with coefficients from functional fields. The first stage of this development of the theory is associated with its founder, J.F. Ritt (1893-1951), and R. Cohn, whose book Difference Algebra (1965) remained the only fundamental monograph on the subject for many years. Nowadays, difference algebra has overgrown the frame of the theory of ordinary algebraic difference equations and appears as a rich theory with applications to the study of equations in finite differences, functional equations, differential equations with delay, algebraic structures with operators, group and semigroup rings.

The monograph is intended for graduate students and researchers in difference and differential algebra, commutative algebra, ring theory, and algebraic geometry. The book is self-contained; it requires no prerequisites other than the knowledge of basic algebraic concepts and a mathematical maturity of an advanced undergraduate.

Why the living world may be the next great frontier of physics The frontiers of physics can seem impossibly remote-located in the invisible quantum realm or the farthest reaches of the cosmos. But one of physics' most exciting frontiers lies much closer than we realize: within our own bodies and other living organisms, which display astonishingly intricate structural patterns and dynamic processes that we don't yet understand. In Living Matter, leading biophysicist Alex Levine explains why unraveling the mysteries of life may ultimately demand a new physics-one that takes full account of the fundamental differences between living and nonliving matter. Life is distinct not only because of its evolutionary history and function, Levine explains, but because it exhibits unique complexities of structure and organizational behavior. In addition, life thrives in states that are not always predictable by means of the same physical principles used to explain nonliving systems. From single proteins to entire collections of cells, and from DNA to the eyes, ears, and brain, Levine tours the most promising areas of life where a new physics might be found. Along the way, he considers many fascinating issues, such as the electrical nature of thought and the emergence of life from the inanimate. Revealing what the study of the biological world can contribute to physics, Living Matter unveils the potential scientific revolution that exists in the uncharted territory lying at, and in, our very fingertips.