This Gedenkschrift for Peter Carr, our dear friend and colleague who suddenly left us on March 1, 2022, was organized to honor the life and lasting contributions of Peter to Quantitative Finance. A group of Peter's co-authors and professional friends contributed chapters for this Gedenkschrift shortly after his passing. The papers were received by September 15, 2022 and some were presented at the Peter Carr Gedenkschrift Conference held at the Robert H Smith School of Business on November 11, 2022. The contributed papers cover a wide range of topics corresponding to the vast range of Peter's interests. Each paper represents new research results in recognition of Peter's scholarly activities. The book serves as an important marker for the research knowledge existing at the time of the Gedenkschrift's publication on a number of topics within quantitative finance. It reflects the diverse interactions between mathematics and finance and illustrates, for those interested, the breadth and depth of this development. The book also presents a collection of tributes to Peter from family and friends including those made at his Memorial Service on March 19, 2022. The result is hopefully a more complete testament to a personal and professional life well lived, and unexpectedly cut short.

This self-contained volume brings together a collection of chapters by some of the most distinguished researchers and practitioners in the fields of mathematical finance and financial engineering. Presenting state-of-the-art developments in theory and practice, the Festschrift is dedicated to Dilip B. Madan on the occasion of his 60th birthday. Specific topics covered include: * Theory and application of the Variance-Gamma process * L?vy process driven fixed-income and credit-risk models, including CDO pricing * Numerical PDE and Monte Carlo methods * Asset pricing and derivatives valuation and hedging * It? formulas for fractional Brownian motion * Martingale characterization of asset price bubbles * Utility valuation for credit derivatives and portfolio management Advances in Mathematical Finance is a valuable resource for graduate students, researchers, and practitioners in mathematical finance and financial engineering. Contributors: H. Albrecher, D. C. Brody, P. Carr, E. Eberlein, R. J. Elliott, M. C. Fu, H. Geman, M. Heidari, A. Hirsa, L. P. Hughston, R. A. Jarrow, X. Jin, W. Kluge, S. A. Ladoucette, A. Macrina, D. B. Madan, F. Milne, M. Musiela, P. Protter, W. Schoutens, E. Seneta, K. Shimbo, R. Sircar, J. van der Hoek, M.Yor, T. Zariphopoulou

'The book is an ideal complement to existing monographs on financial risk management. The reader will benefit from a standard background in no-arbitrage pricing. A tour of risk types and risk management principles is presented in a terse, no-fuss manner. Plenty of pointers to additional literature are given, allowing the interested reader to go deeper into any of the topics presented.'Newsletter of the Bachelier Finance Society The Economic Foundations of Risk Management presents the theory, the practice, and applies this knowledge to provide a forensic analysis of some well-known risk management failures. By doing so, this book introduces a unified framework for understanding how to manage the risk of an individual's or corporation's or financial institution's assets and liabilities. The book is divided into five parts. The first part studies the markets and the assets and liabilities that trade therein. Markets are differentiated based on whether they are competitive or not, frictionless or not (and the type of friction), and actively traded or not. Assets are divided into two types: primary assets and financial derivatives. The second part studies models for determining the risks of the traded assets. Models provided include the Black-Scholes-Merton, the Heath-Jarrow-Morton, and the reduced form model for credit risk. Liquidity risk, operational risk, and trading constraint models are also contained therein. The third part studies the conceptual solution to an individual's, firm's, and bank's risk management problem. This formulation involves solving a complex dynamic programming problem that cannot be applied in practice. Consequently, Part IV investigates how risk management is actually done in practice via the use of diversification, static hedging, and dynamic hedging. Finally, Part V applies these collective insights to six case studies, which are famous risk management failures. These are Penn Square Bank, Metallgesellschaft, Orange County, Barings Bank, Long Term Capital Management, and Washington Mutual. The credit crisis is also discussed to understand how risk management failed for many institutions and why.

This book is a collection of original papers by Robert Jarrow that contributed to significant advances in financial economics. Divided into three parts, Part I concerns option pricing theory and its foundations. The papers here deal with the famous Black-Scholes-Merton model, characterizations of the American put option, and the first applications of arbitrage pricing theory to market manipulation and liquidity risk.Part II relates to pricing derivatives under stochastic interest rates. Included is the paper introducing the famous Heath-Jarrow-Morton (HJM) model, together with papers on topics like the characterization of the difference between forward and futures prices, the forward price martingale measure, and applications of the HJM model to foreign currencies and commodities.Part III deals with the pricing of financial derivatives considering both stochastic interest rates and the likelihood of default. Papers cover the reduced form credit risk model, in particular the original Jarrow and Turnbull model, the Markov model for credit rating transitions, counterparty risk, and diversifiable default risk.

Asset pricing theory yields deep insights into crucial market phenomena such as stock market bubbles. Now in a newly revised and updated edition, this textbook guides the reader through this theory and its applications to markets. The new edition features new results on state dependent preferences, a characterization of market efficiency and a more general presentation of multiple-factor models using only the assumptions of no arbitrage and no dominance. Taking an innovative approach based on martingales, the book presents advanced techniques of mathematical finance in a business and economics context, covering a range of relevant topics such as derivatives pricing and hedging, systematic risk, portfolio optimization, market efficiency, and equilibrium pricing models. For applications to high dimensional statistics and machine learning, new multi-factor models are given. This new edition integrates suicide trading strategies into the understanding of asset price bubbles, greatly enriching the overall presentation and further strengthening the book's underlying theme of economic bubbles. Written by a leading expert in risk management, Continuous-Time Asset Pricing Theory is the first textbook on asset pricing theory with a martingale approach. Based on the author's extensive teaching and research experience on the topic, it is particularly well suited for graduate students in business and economics with a strong mathematical background.

This book teaches the basics of fixed-income securities in a way that, unlike competitive texts, requires a minimum of prerequisites. While other books focus heavily on institutional details of the bond market, all of which could easily be learned "on the job," Jarrow is more concerned with presenting a coherent theoretical framework for understanding all basic models. His unified approach-the Heath Jarrow Morton model-under which all other models are presented as special cases, enhances understanding while avoiding repetition. The author's pricing model is widely used in today's securities industry. In this revised edition, the author has added new chapters to enrich coverage, and has modified the order of chapters slightly to smooth the progression of material from simple to complex. Online material will be available with the text, replacing the diskette included in the first edition; lecture notes for instructors will be available on PowerPoint slides. MathWorks has provided a free online, limited version of the MATLAB's financial derivatives toolbox, with which users of the book can apply the theory presented in each chapter.

'The book is an ideal complement to existing monographs on financial risk management. The reader will benefit from a standard background in no-arbitrage pricing. A tour of risk types and risk management principles is presented in a terse, no-fuss manner. Plenty of pointers to additional literature are given, allowing the interested reader to go deeper into any of the topics presented.'Newsletter of the Bachelier Finance Society The Economic Foundations of Risk Management presents the theory, the practice, and applies this knowledge to provide a forensic analysis of some well-known risk management failures. By doing so, this book introduces a unified framework for understanding how to manage the risk of an individual's or corporation's or financial institution's assets and liabilities. The book is divided into five parts. The first part studies the markets and the assets and liabilities that trade therein. Markets are differentiated based on whether they are competitive or not, frictionless or not (and the type of friction), and actively traded or not. Assets are divided into two types: primary assets and financial derivatives. The second part studies models for determining the risks of the traded assets. Models provided include the Black-Scholes-Merton, the Heath-Jarrow-Morton, and the reduced form model for credit risk. Liquidity risk, operational risk, and trading constraint models are also contained therein. The third part studies the conceptual solution to an individual's, firm's, and bank's risk management problem. This formulation involves solving a complex dynamic programming problem that cannot be applied in practice. Consequently, Part IV investigates how risk management is actually done in practice via the use of diversification, static hedging, and dynamic hedging. Finally, Part V applies these collective insights to six case studies, which are famous risk management failures. These are Penn Square Bank, Metallgesellschaft, Orange County, Barings Bank, Long Term Capital Management, and Washington Mutual. The credit crisis is also discussed to understand how risk management failed for many institutions and why.

Yielding new insights into important market phenomena like asset price bubbles and trading constraints, this is the first textbook to present asset pricing theory using the martingale approach (and all of its extensions). Since the 1970s asset pricing theory has been studied, refined, and extended, and many different approaches can be used to present this material. Existing PhD-level books on this topic are aimed at either economics and business school students or mathematics students. While the first mostly ignore much of the research done in mathematical finance, the second emphasizes mathematical finance but does not focus on the topics of most relevance to economics and business school students. These topics are derivatives pricing and hedging (the Black-Scholes-Merton, the Heath-Jarrow-Morton, and the reduced-form credit risk models), multiple-factor models, characterizing systematic risk, portfolio optimization, market efficiency, and equilibrium (capital asset and consumption) pricing models. This book fills this gap, presenting the relevant topics from mathematical finance, but aimed at Economics and Business School students with strong mathematical backgrounds.