A. Pentland, A.Lipton and T. Hardjono, Building the New Economy: Data as Capital. MIT Press - 2021.

How to empower people and communities with user-centric data ownership, transparent and accountable algorithms, and secure digital transaction systems.

Data is now central to the economy, government, and health systems—so why are data and the AI systems that interpret the data in the hands of so few people? Building the New Economy calls for us to reinvent the ways that data and artificial intelligence are used in civic and government systems. Arguing that we need to think about data as a new type of capital, the authors show use data trusts and distributed ledgers to empower people and communities with user-centric data ownership, transparent and accountable algorithms, machine learning fairness principles and methodologies, and secure digital transaction systems.

It's well known that social media generate disinformation and that mobile phone tracking apps threaten privacy. But these same technologies may also enable the creation of more agile systems in which power and decision-making are distributed among stakeholders rather than concentrated in a few hands. Offering both big ideas and detailed blueprints, the authors describe such key building blocks as data cooperatives, tokenized funding mechanisms, and tradecoin architecture. They also discuss technical issues, including how to build an ecosystem of trusted data, the implementation of digital currencies, and interoperability, and consider the evolution of computational law systems.

A. Itkin, A.Lipton and D. Muravey, Generalized Integral Transforms in Mathematical Finance. World Scientific Publishing Co. - 2021.

This book describes several techniques, first invented in physics for solving problems of heat and mass transfer, and applies them to various problems of mathematical finance defined in domains with moving boundaries. These problems include: (a) semi-closed form pricing of options in the one-factor models with time-dependent barriers (Bachelier, Hull-White, CIR, CEV); (b) analyzing an interconnected banking system in the structural credit risk model with default contagion; (c) finding first hitting time density for a reducible diffusion process; (d) describing the exercise boundary of American options; (e) calculating default boundary for the structured default problem; (f) deriving a semi-closed form solution for optimal mean-reverting trading strategies; to mention but some.

The main methods used in this book are generalized integral transforms and heat potentials. To find a semi-closed form solution, we need to solve a linear or nonlinear Volterra equation of the second kind and then represent the option price as a one-dimensional integral. Our analysis shows that these methods are computationally more efficient than the corresponding finite-difference methods for the backward or forward Kolmogorov PDEs (partial differential equations) while providing better accuracy and stability.

We extend a large number of known results by either providing solutions on complementary or extended domains where the solution is not known yet or modifying these techniques and applying them to new types of equations, such as the Bessel process. The book contains several novel results broadly applicable in physics, mathematics, and engineering.

A.Lipton and A. Treccani, Blockchain and Distributed Ledgers: Mathematics, Technology, and Economics. World Scientific Publishing Co. - 2021.

This textbook focuses on distributed ledger technology (DLT) and its potential impact on society at large. The book aims to offer a detailed and self-contained introduction to the founding principles behind DLT accessible to a well-educated but not necessarily mathematically-oriented audience. DLT, which became extremely popular over the last decade, allows solving many complicated problems arising in economics, banking, and finance, industry, trade, and other fields. DLT accomplishes these tasks by developing new mechanisms for distributed consensus, using advanced tools from cryptography, game theory, economics, finance, scientific computing, and others. DLT offers optimal and elegant solutions in many situations. However, to reap the ultimate benefits, one has to overcome some of its inherent limitations and use it judiciously. Not surprisingly, amid increasing applications of DLT, misconceptions are formed over its use, not least because numerous authors identify it with cryptocurrencies such as Bitcoin, Ethereum, Ripple, and their numerous extensions. This situation calls for an impartial assessment of the situation rooted in scientific reasoning, rather than speculation, enthusiastic naivete and personal attacks on one's opponents.

Blockchain and Distributed Ledgers: Mathematics, Technology, and Economics offers a detailed and self-contained introduction to DLT, blockchains, and cryptocurrencies. The book guides the reader through the development and building up of a distributed ledger suitable for one's interest. It covers the basics of cryptography and its applications to cryptocurrencies; provides historical examples of centralized cryptocurrencies; discusses theoretical foundations of decentralized cryptocurrencies, including game theory aspects and Byzantine fault-tolerant consensus; explains operational features of Bitcoin trading platform, including storage, mining, and wallets; covers alternative platforms, including Ethereum, Ripple, Stellar, Zcash, and others; defines smart contracts; covers potential financial and non-financial applications of decentralized ledgers with a detailed analysis of their pros and cons. This introductory text seeks to equip the reader with an ability to participate in the crypto economy meaningfully.

A.Lipton, Financial Engineering. Selected Works of Alexander Lipton. World Scientific Publishing Co. - 2018.

Edited by Alexander Lipton (Quant of the Year, 2000), this volume is a collection of Lipton's important and original papers on financial engineering written over his 20-year career as a preeminent quant working for leading financial institutions in New York, Chicago, and London. The papers cover topics ranging from the volatility smile problem, credit risk, macroeconomics and monetary circuit, and exotic options, summarizing Lipton's fundamental contributions to these areas.

In addition to papers published in leading academic and practitioner-oriented journals, this volume contains a detailed introduction and two previously unpublished chapters. Some of the seminal papers in this book cover local-stochastic volatility models, passport options, credit value adjustments for credit default swaps, and asymptotics for exponential Lévy processes and their volatility smile.

Alexander Lipton is one of the most respected quants of his generation and the first recipient of the prestigious Quant of the Year award by Risk Magazine.

A.Lipton, Quant of the Year 2000 - 2014. All the Award Winning Papers. Risk Books - 2014.

Quant of the Year 2000-2014 will empower readers to become familiar with the most important ideas regarding financial engineering presented since the year 2000, including the theoretical and practical answers to the problems posed by the financial crisis and its aftermath. Readers will learn how the best quants think and operate, what the most significant problems of the general field of financial engineering have been, and how to deal with the most important problems the quant community is now facing.

A.Lipton and A. Rennie, The Oxford Handbook of Credit Derivatives. Oxford University Press - 2011.

From the late 1990s, the spectacular growth of a secondary market for credit through derivatives has been matched by the emergence of mathematical modelling analysing the credit risk embedded in these contracts. This book aims to provide a broad and deep overview of this modelling, covering statistical analysis and techniques, modelling of default of both single and multiple entities, counterparty risk, Gaussian and non-Gaussian modelling, and securitisation. Both reduced-form and firm-value models for the default of single entities are considered in detail, with extensive discussion of both their theoretical underpinnings and their practical usage in pricing and risk. For multiple entity modelling, the now-notorious Gaussian copula is discussed, with analysis of its shortcomings, as well as a wide range of alternative approaches, including multivariate extensions to both firm-value and reduced form models, and continuous-time Markov chains. One important case of multiple entities modelling – counterparty risk in credit derivatives – is further explored, in two dedicated articles. Alternative non-Gaussian approaches to modelling are also discussed, including extreme-value theory and saddle-point approximations to deal with tail risk. Finally, the recent growth in securitisation is covered, including house price modelling and pricing models for asset-backed CDOs. The current credit crisis has brought modelling of the previously arcane credit markets into the public arena. This book provides discussion of the mathematical modelling that underpins both credit derivatives and securitisation. Though technical in nature, the pros and cons of various approaches attempt to provide a balanced view of the role that mathematical modelling plays in the modern credit markets.

A.Lipton, Theory and Practice of Credit Risk Modelling. Risk Books - 2008.

The rise of credit markets over the past decade has been nothing short of spectacular. Their current state of turmoil is nothing short of mind-boggling. It seems to be а perfect moment for putting together an authoritative collection of papers devoted to various intertwining aspects of credit modelling. Such а collection would benefit both practitioners and academics working in this area. It could also be used by students of the subject. Arguably, credit modelling is the most difficult area of financial engineering, and is often recognised as such. Hence, it is not а coincidence that out of 32 authors whose work is published in the present volume, one (Oldrich Vasicek) received а Lifetime Achievement Award, and five (Leif Andersen, Мichael Gordy, Alexander Lipton, Richard Martin, and Philip Schonbucher) received Quant of the Year Awards from Risk.

A.Lipton and A. Rennie, Credit Correlations. Life after Copulas. World Scientific Publishing Co. - 2008.

The recent growth of credit derivatives has been explosive. The global credit derivatives market grew in notional value from $1 trillion to $20 trillion from 2000 to 2006. However, understanding the true nature of these instruments still poses both theoretical and practical challenges. For a long time now, the framework of Gaussian copulas parameterized by correlation, and more recently base correlation, has provided an adequate, if unintuitive, description of the market. However, the increased liquidity in credit indices and index tranches, as well as the proliferation of exotic instruments such as forward starting tranches, options on tranches, leveraged super senior tranches, and the like, have made it imperative to come up with models that describe market reality better.

This book, originally and concurrently published in the International Journal of Theoretical and Applied Finance, Vol. 10, No. 4, 2007, agrees that base correlation has outlived its usefulness; opinions of how to replace it, however, are divided. Both the top-down and bottom-up approaches for describing the dynamics of credit baskets are presented, and pro and contra arguments are put forward. Readers will decide which direction is the most promising one at the moment. However, it is hoped that, in the near future, models that transcend base correlation will be proposed and accepted by the market.

A.Lipton, Exotic Options. The Cutting Edge Collection. Risk Books - 2008.

A.Lipton, Mathematical Methods for Foreign Exchange. World Scientific Publishing Co. - 2001.

This comprehensive book presents a systematic and practically oriented approach to mathematical modeling in finance, particularly in the foreign exchange context. It describes all the relevant aspects of financial engineering, including derivative pricing, in detail. The book is self-contained, with the necessary mathematical, economic, and trading background carefully explained. In addition to the lucid treatment of the standard material, it describes many original results.

The book can be used both as a text for students of financial engineering, and as a basic reference for risk managers, traders, and academics.

A.Lipton (A. Lifschitz), Magnetohydrodynamics and Spectral Theory. Springer - 1989.

Magnetohydrodynamics gives an adequate description of motions of conducting fluids as well as of slow, large scale motions of magnetized plasmas. It lends itself as a powerful tool for solving a number of important problems in astrophysics, planetary physics and engineering. In particular, magneto hydrodynamics can be successfully used in controlled thermonuclear fusion studies. This book is devoted to various spectral problems arising in a magnetohydrodynamic context. Equal emphasis is placed on physical and mathematical questions where both stable and unstable modes are treated. The book will be of primary interest to research workers in plasma and space physics, but will also appeal to students undertaking a course in MHD, with a strong mathematical bias.