Author: Pierre Bernhard Publisher: Springer Science & Business Media ISBN: 0817683887 Category : Mathematics Languages : en Pages : 348
Book Description
Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance. These theories did away with the standard stochastic geometric diffusion “Samuelson” market model (also known as the Black-Scholes model because it is used in that most famous theory), instead opting for models that allowed minimax approaches to complement or replace stochastic methods. Among the most fruitful models were those utilizing game-theoretic tools and the so-called interval market model. Over time, these models have slowly but steadily gained influence in the financial community, providing a useful alternative to classical methods. A self-contained monograph, The Interval Market Model in Mathematical Finance: Game-Theoretic Methods assembles some of the most important results, old and new, in this area of research. Written by seven of the most prominent pioneers of the interval market model and game-theoretic finance, the work provides a detailed account of several closely related modeling techniques for an array of problems in mathematical economics. The book is divided into five parts, which successively address topics including: · probability-free Black-Scholes theory; · fair-price interval of an option; · representation formulas and fast algorithms for option pricing; · rainbow options; · tychastic approach of mathematical finance based upon viability theory. This book provides a welcome addition to the literature, complementing myriad titles on the market that take a classical approach to mathematical finance. It is a worthwhile resource for researchers in applied mathematics and quantitative finance, and has also been written in a manner accessible to financially-inclined readers with a limited technical background.
Author: Emil Dinga Publisher: Taylor & Francis ISBN: 1000609693 Category : Business & Economics Languages : en Pages : 299
Book Description
This book addresses the functioning of financial markets, in particular the financial market model, and modelling. More specifically, the book provides a model of adaptive preference in the financial market, rather than the model of the adaptive financial market, which is mostly based on Popper's objective propensity for the singular, i.e., unrepeatable, event. As a result, the concept of preference, following Simon's theory of satisficing, is developed in a logical way with the goal of supplying a foundation for a robust theory of adaptive preference in financial market behavior. The book offers new insights into financial market logic, and psychology: 1) advocating for the priority of behavior over information - in opposition to traditional financial market theories; 2) constructing the processes of (co)evolution adaptive preference-financial market using the concept of fetal reaction norms - between financial market and adaptive preference; 3) presenting a new typology of information in the financial market, aimed at proving point (1) above, as well as edifying an explicative mechanism of the evolutionary nature and behavior of the (real) financial market; 4) presenting sufficient, and necessary, principles or assumptions for developing a theory of adaptive preference in the financial market; and 5) proposing a new interpretation of the pair genotype-phenotype in the financial market model. The book's distinguishing feature is its research method, which is mainly logically rather than historically or empirically based. As a result, the book is targeted at generating debate about the best and most scientifically beneficial method of approaching, analyzing, and modelling financial markets.
Author: Vasily N Kolokoltsov Publisher: World Scientific ISBN: 9811214875 Category : Mathematics Languages : en Pages : 411
Book Description
Steadily growing applications of game theory in modern science (including psychology, biology and economics) require sources to provide rapid access in both classical tools and recent developments to readers with diverse backgrounds. This book on game theory, its applications and mathematical methods, is written with this objective in mind.The book gives a concise but wide-ranging introduction to games including older (pre-game theory) party games and more recent topics like elections and evolutionary games and is generously spiced with excursions into philosophy, history, literature and politics. A distinguished feature is the clear separation of the text into two parts: elementary and advanced, which makes the book ideal for study at various levels.Part I displays basic ideas using no more than four arithmetic operations and requiring from the reader only some inclination to logical thinking. It can be used in a university degree course without any (or minimal) prerequisite in mathematics (say, in economics, business, systems biology), as well as for self-study by school teachers, social and natural scientists, businessmen or laymen. Part II is a rapid introduction to the mathematical methods of game theory, suitable for a mathematics degree course of various levels.To stimulate the mathematical and scientific imagination, graphics by a world-renowned mathematician and mathematics imaging artist, A T Fomenko, are used. The carefully selected works of this artist fit remarkably into the many ideas expressed in the book.This new edition has been updated and enlarged. In particular, two new chapters were added on statistical limit of games with many agents and on quantum games, reflecting possibly the two most stunning trends in the game theory of the 21st century.
Author: Didier Sornette Publisher: Springer Science & Business Media ISBN: 3642279317 Category : Business & Economics Languages : en Pages : 260
Book Description
The current financial crisis has revealed serious flaws in models, measures and, potentially, theories, that failed to provide forward-looking expectations for upcoming losses originated from market risks. The Proceedings of the Perm Winter School 2011 propose insights on many key issues and advances in financial markets modeling and risk measurement aiming to bridge the gap. The key addressed topics include: hierarchical and ultrametric models of financial crashes, dynamic hedging, arbitrage free modeling the term structure of interest rates, agent based modeling of order flow, asset pricing in a fractional market, hedge funds performance and many more.
Author: Dmitrii S. Silvestrov Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110329840 Category : Mathematics Languages : en Pages : 572
Book Description
The book gives a systematical presentation of stochastic approximation methods for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The volume presents results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies.
Author: Jaksa Cvitanic Publisher: MIT Press ISBN: 9780262033206 Category : Business & Economics Languages : en Pages : 528
Book Description
An innovative textbook for use in advanced undergraduate and graduate courses; accessible to students in financial mathematics, financial engineering and economics. Introduction to the Economics and Mathematics of Financial Markets fills the longstanding need for an accessible yet serious textbook treatment of financial economics. The book provides a rigorous overview of the subject, while its flexible presentation makes it suitable for use with different levels of undergraduate and graduate students. Each chapter presents mathematical models of financial problems at three different degrees of sophistication: single-period, multi-period, and continuous-time. The single-period and multi-period models require only basic calculus and an introductory probability/statistics course, while an advanced undergraduate course in probability is helpful in understanding the continuous-time models. In this way, the material is given complete coverage at different levels; the less advanced student can stop before the more sophisticated mathematics and still be able to grasp the general principles of financial economics. The book is divided into three parts. The first part provides an introduction to basic securities and financial market organization, the concept of interest rates, the main mathematical models, and quantitative ways to measure risks and rewards. The second part treats option pricing and hedging; here and throughout the book, the authors emphasize the Martingale or probabilistic approach. Finally, the third part examines equilibrium models—a subject often neglected by other texts in financial mathematics, but included here because of the qualitative insight it offers into the behavior of market participants and pricing.
Author: Jean-Pierre Aubin Publisher: Springer ISBN: 3319081292 Category : Mathematics Languages : en Pages : 136
Book Description
This book presents a forecasting mechanism of the price intervals for deriving the SCR (solvency capital requirement) eradicating the risk during the exercise period on one hand and measuring the risk by computing the hedging exit time function associating with smaller investments the date until which the value of the portfolio hedges the liabilities on the other. This information, summarized under the term “tychastic viability measure of risk” is an evolutionary alternative to statistical measures, when dealing with evolutions under uncertainty. The book is written by experts in the field and the target audience primarily comprises research experts and practitioners.
Author: Alexey N. Karapetyants Publisher: Springer Nature ISBN: 3030768295 Category : Mathematics Languages : en Pages : 413
Book Description
This volume is part of the collaboration agreement between Springer and the ISAAC society. This is the second in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University, Rostov-on-Don, Russia. This volume focuses on mathematical methods and applications of probability and statistics in the context of general harmonic analysis and its numerous applications. The two volumes cover new trends and advances in several very important fields of mathematics, developed intensively over the last decade. The relevance of this topic is related to the study of complex multi-parameter objects required when considering operators and objects with variable parameters.
Author: Nikolai Dokuchaev Publisher: Routledge ISBN: 1134121989 Category : Business & Economics Languages : en Pages : 197
Book Description
Rigorous in style, yet easy to use, this comprehensive textbook offers a systematic, self-sufficient yet concise presentation of the main topics and related parts of Stochastic Analysis and statistical finance covered in most degree courses.
Author: Jean-Pierre Aubin Publisher: Springer Science & Business Media ISBN: 3319000055 Category : Business & Economics Languages : en Pages : 155
Book Description
This authored monograph presents an unconventional approach to an important topic in economic theory. The author is an expert in the field of viability theory and applies this theory to analyze how an economy should be dynamically endowed so that it is economically viable. Economic viability requires an assumption on the joint evolution of transactions, fluctuations of prices and units of numeraire goods: the sum of the “transactions values” and the “impact of price fluctuations” should be negative or equal to zero. The book presents a computation of the minimum endowment which restores economic viability and derives the dynamic laws that regulate both transactions and price fluctuations. The target audience primarily comprises open-minded and mathematically interested economists but the book may also be beneficial for graduate students.
Author: Pierre Bernhard
Author: Emil Dinga
Author: Vasily N Kolokoltsov
Author: Didier Sornette
Author: Dmitrii S. Silvestrov
Author: Jaksa Cvitanic
Author: Jean-Pierre Aubin
Author: Alexey N. Karapetyants
Author: Nikolai Dokuchaev
Author: Jean-Pierre Aubin