Alexander Melnikov

Adam Day

Bakhadyr Khoussainov

Noam Greenberg

Michael Fellows

Frances Rosamond

This Festschrift is published in honor of Rodney G. Downey, eminent logician and computer scientist, surfer and Scottish country dancer, on the occasion of his 60th birthday. The Festschrift contains papers and laudations that showcase the broad and important scientific, leadership and mentoring contributions made by Rod during his distinguished career. The volume contains 42 papers presenting original unpublished research, or expository and survey results in Turing degrees, computably enumerable sets, computable algebra, computable model theory, algorithmic randomness, reverse mathematics, and parameterized complexity, all areas in which Rod Downey has had significant interests and influence. The volume contains several surveys that make the various areas accessible to non-specialists while also including some proofs that illustrate the flavor of the fields.

Essays Dedicated to Rodney G. Downey on the Occasion of His 60th Birthday

Computability and Complexity

Rodney G. Downey

This is the first book which gives a unified theory for countable and uncountable computable structures. The work treats computable linear orderings, graphs, groups and Boolean algebras unified with computable metric and Banach spaces, profinite groups, and the like. Further, it provides the first account of these that exploits effective versions of dualities, such as Stone and Pontryagin dualities. The themes are effective classification and enumeration. Topics and features: !-- [if !supportLists]--· !--[endif]--Delivers a self-contained, gentle introduction to priority arguments, directly applying them in algebraic contexts !-- [if !supportLists]--· !--[endif]--Includes extensive exercises that both cement and amplify the materials !-- [if !supportLists]--· !--[endif]--Provides complete introduction to the basics of computable analysis, particularly in the context of computable structures !-- [if !supportLists]--· !--[endif]--Offers the first monograph treatment of computable Polish groups, effective profinite groups via Stone duality, and effective abelian groups via Pontryagin duality !-- [if !supportLists]--· !--[endif]--Presents the first book treatment of Friedberg enumerations of structures This unique volume is aimed at graduate students and researchers in computability theory, as well as mathematicians seeking to understand the algorithmic content of structure theory. Being self-contained, it provides ample opportunity for self-study.

A Unified Approach

Computable Structure Theory

Mohamed Abdelghani

It is well-known that modern stochastic calculus has been exhaustively developed under usual conditions. Despite such a well-developed theory, there is evidence to suggest that these very convenient technical conditions cannot necessarily be fulfilled in real-world applications. Optional Processes: Theory and Applications seeks to delve into the existing theory, new developments and applications of optional processes on "unusual" probability spaces. The development of stochastic calculus of optional processes marks the beginning of a new and more general form of stochastic analysis. This book aims to provide an accessible, comprehensive and up-to-date exposition of optional processes and their numerous properties. Furthermore, the book presents not only current theory of optional processes, but it also contains a spectrum of applications to stochastic differential equations, filtering theory and mathematical finance. Features Suitable for graduate students and researchers in mathematical finance, actuarial science, applied mathematics and related areas Compiles almost all essential results on the calculus of optional processes in unusual probability spaces Contains many advanced analytical results for stochastic differential equations and statistics pertaining to the calculus of optional processes Develops new methods in finance based on optional processes such as a new portfolio theory, defaultable claim pricing mechanism, etc. Authors Mohamed Abdelghani completed his PhD in mathematical finance from the University of Alberta, Edmonton, Canada. He is currently working as a vice president in quantitative finance and machine learning at Morgan Stanley, New York, USA. Alexander Melnikov is a professor in mathematical finance at the University of Alberta. His research interests belong to the area of contemporary stochastic analysis and its numerous applications in mathematical finance, statistics and actuarial science. He has written six books as well as over 100 research papers in leading academic journals.

Theory and Applications

Optional Processes

Historically, financial and insurance risks were separate subjects most often analyzed using qualitative methods. The development of quantitative methods based on stochastic analysis is an important achievement of modern financial mathematics, one that can naturally be extended and applied in actuarial mathematics. Risk Analysis in Finance and Insurance offers the first comprehensive and accessible introduction to the ideas, methods, and probabilistic models that have transformed risk management into a quantitative science and led to unified methods for analyzing insurance and finance risks. The author's approach is based on a methodology for estimating the present value of future payments given current financial, insurance, and other information, which leads to proper, practical definitions of the price of a financial contract, the premium for an insurance policy, and the reserve of an insurance company. Self-contained and full of exercises and worked examples, Risk Analysis in Finance and Insurance serves equally well as a text for courses in financial and actuarial mathematics and as a valuable reference for financial analysts and actuaries. Ancillary electronic materials will be available for download from the publisher's Web site.

Alexander Melnikov

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