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Author: Hans Föllmer
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110463458
Category : Mathematics
Languages : en
Pages : 608
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Book Description
This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry. The focus on stochastic models in discrete time has two immediate benefits. First, the probabilistic machinery is simpler, and one can discuss right away some of the key problems in the theory of pricing and hedging of financial derivatives. Second, the paradigm of a complete financial market, where all derivatives admit a perfect hedge, becomes the exception rather than the rule. Thus, the need to confront the intrinsic risks arising from market incomleteness appears at a very early stage. The first part of the book contains a study of a simple one-period model, which also serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of financial risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. This fourth, newly revised edition contains more than one hundred exercises. It also includes material on risk measures and the related issue of model uncertainty, in particular a chapter on dynamic risk measures and sections on robust utility maximization and on efficient hedging with convex risk measures. Contents: Part I: Mathematical finance in one period Arbitrage theory Preferences Optimality and equilibrium Monetary measures of risk Part II: Dynamic hedging Dynamic arbitrage theory American contingent claims Superhedging Efficient hedging Hedging under constraints Minimizing the hedging error Dynamic risk measures
Author: Hans Föllmer
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110463458
Category : Mathematics
Languages : en
Pages : 608
Get Book Here
Book Description
This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry. The focus on stochastic models in discrete time has two immediate benefits. First, the probabilistic machinery is simpler, and one can discuss right away some of the key problems in the theory of pricing and hedging of financial derivatives. Second, the paradigm of a complete financial market, where all derivatives admit a perfect hedge, becomes the exception rather than the rule. Thus, the need to confront the intrinsic risks arising from market incomleteness appears at a very early stage. The first part of the book contains a study of a simple one-period model, which also serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of financial risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. This fourth, newly revised edition contains more than one hundred exercises. It also includes material on risk measures and the related issue of model uncertainty, in particular a chapter on dynamic risk measures and sections on robust utility maximization and on efficient hedging with convex risk measures. Contents: Part I: Mathematical finance in one period Arbitrage theory Preferences Optimality and equilibrium Monetary measures of risk Part II: Dynamic hedging Dynamic arbitrage theory American contingent claims Superhedging Efficient hedging Hedging under constraints Minimizing the hedging error Dynamic risk measures
Author: Kathrin Glau
Publisher: Springer
ISBN: 331909114X
Category : Mathematics
Languages : en
Pages : 434
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Book Description
Quantitative models are omnipresent –but often controversially discussed– in todays risk management practice. New regulations, innovative financial products, and advances in valuation techniques provide a continuous flow of challenging problems for financial engineers and risk managers alike. Designing a sound stochastic model requires finding a careful balance between parsimonious model assumptions, mathematical viability, and interpretability of the output. Moreover, data requirements and the end-user training are to be considered as well. The KPMG Center of Excellence in Risk Management conference Risk Management Reloaded and this proceedings volume contribute to bridging the gap between academia –providing methodological advances– and practice –having a firm understanding of the economic conditions in which a given model is used. Discussed fields of application range from asset management, credit risk, and energy to risk management issues in insurance. Methodologically, dependence modeling, multiple-curve interest rate-models, and model risk are addressed. Finally, regulatory developments and possible limits of mathematical modeling are discussed.
Author: Radu Sebastian Tunaru
Publisher: World Scientific
ISBN: 9814663425
Category : Business & Economics
Languages : en
Pages : 382
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Book Description
The financial systems in most developed countries today build up a large amount of model risk on a daily basis. However, this is not particularly visible as the financial risk management agenda is still dominated by the subprime-liquidity crisis, the sovereign crises, and other major political events. Losses caused by model risk are hard to identify and even when they are internally identified, as such, they are most likely to be classified as normal losses due to market evolution.Model Risk in Financial Markets: From Financial Engineering to Risk Management seeks to change the current perspective on model innovation, implementation and validation. This book presents a wide perspective on model risk related to financial markets, running the gamut from financial engineering to risk management, from financial mathematics to financial statistics. It combines theory and practice, both the classical and modern concepts being introduced for financial modelling. Quantitative finance is a relatively new area of research and much has been written on various directions of research and industry applications. In this book the reader gradually learns to develop a critical view on the fundamental theories and new models being proposed.
Author: Huyên Pham
Publisher: Springer Science & Business Media
ISBN: 3540895000
Category : Mathematics
Languages : en
Pages : 243
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Book Description
Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.
Author: Pierre Henry-Labordere
Publisher: CRC Press
ISBN: 1351666231
Category : Mathematics
Languages : en
Pages : 190
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Book Description
Model-free Hedging: A Martingale Optimal Transport Viewpoint focuses on the computation of model-independent bounds for exotic options consistent with market prices of liquid instruments such as Vanilla options. The author gives an overview of Martingale Optimal Transport, highlighting the differences between the optimal transport and its martingale counterpart. This topic is then discussed in the context of mathematical finance.
Author: Joachim Rosenthal
Publisher: Springer Science & Business Media
ISBN: 0387216960
Category : Science
Languages : en
Pages : 508
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Book Description
This volume contains survey and research articles by some of the leading researchers in mathematical systems theory - a vibrant research area in its own right. Many authors have taken special care that their articles are self-contained and accessible also to non-specialists.
Author: Sigrid Müller
Publisher: Springer Science & Business Media
ISBN: 3642465609
Category : Law
Languages : en
Pages : 160
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Book Description
Author: Shige Peng
Publisher: Springer Nature
ISBN: 3662599031
Category : Mathematics
Languages : en
Pages : 216
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Book Description
This book is focused on the recent developments on problems of probability model uncertainty by using the notion of nonlinear expectations and, in particular, sublinear expectations. It provides a gentle coverage of the theory of nonlinear expectations and related stochastic analysis. Many notions and results, for example, G-normal distribution, G-Brownian motion, G-Martingale representation theorem, and related stochastic calculus are first introduced or obtained by the author. This book is based on Shige Peng’s lecture notes for a series of lectures given at summer schools and universities worldwide. It starts with basic definitions of nonlinear expectations and their relation to coherent measures of risk, law of large numbers and central limit theorems under nonlinear expectations, and develops into stochastic integral and stochastic calculus under G-expectations. It ends with recent research topic on G-Martingale representation theorem and G-stochastic integral for locally integrable processes. With exercises to practice at the end of each chapter, this book can be used as a graduate textbook for students in probability theory and mathematical finance. Each chapter also concludes with a section Notes and Comments, which gives history and further references on the material covered in that chapter. Researchers and graduate students interested in probability theory and mathematical finance will find this book very useful.
Author: Robert Buff
Publisher: Springer Science & Business Media
ISBN: 3642563236
Category : Mathematics
Languages : en
Pages : 246
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Book Description
This is one of the only books to describe uncertain volatility models in mathematical finance and their computer implementation for portfolios of vanilla, barrier and American options in equity and FX markets. Uncertain volatility models place subjective constraints on the volatility of the stochastic process of the underlying asset and evaluate option portfolios under worst- and best-case scenarios. This book, which is bundled with software, is aimed at graduate students, researchers and practitioners who wish to study advanced aspects of volatility risk in portfolios of vanilla and exotic options. The reader is assumed to be familiar with arbitrage pricing theory.
Author: Akihiko Takahashi
Publisher: World Scientific
ISBN: 9814407348
Category : Mathematics
Languages : en
Pages : 231
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Book Description
This book is the Proceedings of the International Workshop on Finance 2011, held in Kyoto in the summer of 2011 with the aim of exchanging new ideas in financial engineering among researchers from various countries from both academia and industry. The workshop was held as a successor to the Daiwa International Workshop (2004-2008), and the KIER-TMU International Workshop (2009-2010). This workshop was organized by the Center for Advanced Research in Finance (CARF), Graduate School of Economics, the University of Tokyo, and Graduate School of Social Sciences, Tokyo Metropolitan University — and co-organized by Life Risk Research Center, Doshisha University.The workshop serves as a bridge between academic researchers and practitioners. This book contains about fifteen papers, all refereed, representing the presentations at the workshop. The papers address state-of-the-art techniques in financial engineering.
