Convex Duality And Financial Mathematics

Author : Peter Carr,Qiji Jim Zhu
Publisher : Springer
Page : 152 pages
File Size : 53,9 Mb
Release : 2018-07-18
Category : Mathematics
ISBN : 9783319924922

Get Book

Convex Duality and Financial Mathematics by Peter Carr,Qiji Jim Zhu Pdf

This book provides a concise introduction to convex duality in financial mathematics. Convex duality plays an essential role in dealing with financial problems and involves maximizing concave utility functions and minimizing convex risk measures. Recently, convex and generalized convex dualities have shown to be crucial in the process of the dynamic hedging of contingent claims. Common underlying principles and connections between different perspectives are developed; results are illustrated through graphs and explained heuristically. This book can be used as a reference and is aimed toward graduate students, researchers and practitioners in mathematics, finance, economics, and optimization. Topics include: Markowitz portfolio theory, growth portfolio theory, fundamental theorem of asset pricing emphasizing the duality between utility optimization and pricing by martingale measures, risk measures and its dual representation, hedging and super-hedging and its relationship with linear programming duality and the duality relationship in dynamic hedging of contingent claims

Author : Marco Frittelli,Sara Biagini
Publisher : Springer
Page : 186 pages
File Size : 46,8 Mb
Release : 2007
Category : Mathematics
ISBN : 3540401083

Get Book

Duality in Mathematical Finance by Marco Frittelli,Sara Biagini Pdf

This monograph presents an advanced and unified treatment of four important issues that have dominated the theoretical research in mathematical finance for the last ten years: (1) the fundamental theorem of asset pricing; (2) utility maximization in incomplete markets; (3) pricing in incomplete markets; (4) the risk measurement of a static payoff and of a cash-flow stream. The powerful tools of convex analysis and duality theory are systematically applied to investigate these topics, under very general assumptions on the financial markets. This duality approach reveals the prominent role of the investor’s preferences in all these fundamental issues and contributes to a deeper understanding of the economic aspects of the theory.

Author : Radu Ioan-Bot
Publisher : Springer
Page : 164 pages
File Size : 54,9 Mb
Release : 2011-03-03
Category : Business & Economics
ISBN : 364204915X

Get Book

Conjugate Duality in Convex Optimization by Radu Ioan-Bot Pdf

The results presented in this book originate from the last decade research work of the author in the ?eld of duality theory in convex optimization. The reputation of duality in the optimization theory comes mainly from the major role that it plays in formulating necessary and suf?cient optimality conditions and, consequently, in generatingdifferent algorithmic approachesfor solving mathematical programming problems. The investigations made in this work prove the importance of the duality theory beyond these aspects and emphasize its strong connections with different topics in convex analysis, nonlinear analysis, functional analysis and in the theory of monotone operators. The ?rst part of the book brings to the attention of the reader the perturbation approach as a fundamental tool for developing the so-called conjugate duality t- ory. The classical Lagrange and Fenchel duality approaches are particular instances of this general concept. More than that, the generalized interior point regularity conditions stated in the past for the two mentioned situations turn out to be p- ticularizations of the ones given in this general setting. In our investigations, the perturbationapproachrepresentsthestartingpointforderivingnewdualityconcepts for several classes of convex optimization problems. Moreover, via this approach, generalized Moreau–Rockafellar formulae are provided and, in connection with them, a new class of regularity conditions, called closedness-type conditions, for both stable strong duality and strong duality is introduced. By stable strong duality we understand the situation in which strong duality still holds whenever perturbing the objective function of the primal problem with a linear continuous functional.

Author : Ivar Ekeland,Roger Temam
Publisher : SIAM
Page : 414 pages
File Size : 42,6 Mb
Release : 1999-12-01
Category : Mathematics
ISBN : 161197108X

Get Book

Convex Analysis and Variational Problems by Ivar Ekeland,Roger Temam Pdf

This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.

Author : Ioannis Karatzas
Publisher : American Mathematical Society(RI)
Page : 172 pages
File Size : 52,9 Mb
Release : 1997
Category : Business mathematics
ISBN : UOM:39076001803936

Get Book

Lectures on the Mathematics of Finance by Ioannis Karatzas Pdf

In this text, the author discusses the main aspects of mathematical finance. These include arbitrage, hedging and pricing of contingent claims, portfolio optimization, incomplete and/or constrained markets, equilibrium, and transaction costs. The book outlines advances made possible during the last fifteen years due to the methodologies of stochastic analysis and control. Readers are presented with current research, and open problems are suggested. This tutorial survey of the rapidly expanding field of mathematical finance is addressed primarily to graduate students in mathematics. Familiarity is assumed with stochastic analysis and parabolic partial differential equations. The text makes significant use of students' mathematical skills, but always in connection with interesting applied problems.

Author : Mladen Victor Wickerhauser
Publisher : CRC Press
Page : 305 pages
File Size : 43,8 Mb
Release : 2022-11-09
Category : Mathematics
ISBN : 9781000778816

Get Book

Introducing Financial Mathematics by Mladen Victor Wickerhauser Pdf

Introducing Financial Mathematics: Theory, Binomial Models, and Applications seeks to replace existing books with a rigorous stand-alone text that covers fewer examples in greater detail with more proofs. The book uses the fundamental theorem of asset pricing as an introduction to linear algebra and convex analysis. It also provides example computer programs, mainly Octave/MATLAB functions but also spreadsheets and Macsyma scripts, with which students may experiment on real data.The text's unique coverage is in its contemporary combination of discrete and continuous models to compute implied volatility and fit models to market data. The goal is to bridge the large gaps among nonmathematical finance texts, purely theoretical economics texts, and specific software-focused engineering texts.

Author : Sorin-Mihai Grad
Publisher : Springer
Page : 282 pages
File Size : 44,9 Mb
Release : 2014-09-03
Category : Business & Economics
ISBN : 9783319089003

Get Book

Vector Optimization and Monotone Operators via Convex Duality by Sorin-Mihai Grad Pdf

This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classical ones is proposed. Moreover, the book addresses different efficiency concepts for vector optimization problems. Among the problems that appear when the framework is generalized by considering set-valued functions, an increasing interest is generated by those involving monotone operators, especially now that new methods for approaching them by means of convex analysis have been developed. Following this path, the book provides several results on different properties of sums of monotone operators.

Author : David P. Ellerman
Publisher : Rowman & Littlefield
Page : 296 pages
File Size : 55,6 Mb
Release : 1995
Category : Business & Economics
ISBN : 0847679322

Get Book

Intellectual Trespassing as a Way of Life by David P. Ellerman Pdf

Dramatic changes or revolutions in a field of science are often made by outsiders or 'trespassers, ' who are not limited by the established, 'expert' approaches. Each essay in this diverse collection shows the fruits of intellectual trespassing and poaching among fields such as economics, Kantian ethics, Platonic philosophy, category theory, double-entry accounting, arbitrage, algebraic logic, series-parallel duality, and financial arithmetic.

Author : Olivier Gueant
Publisher : CRC Press
Page : 302 pages
File Size : 48,7 Mb
Release : 2016-03-30
Category : Business & Economics
ISBN : 9781498725484

Get Book

The Financial Mathematics of Market Liquidity by Olivier Gueant Pdf

This book is among the first to present the mathematical models most commonly used to solve optimal execution problems and market making problems in finance. The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making presents a general modeling framework for optimal execution problems-inspired from the Almgren-Chriss app

Author : Xinmin Yang
Publisher : Springer
Page : 167 pages
File Size : 53,8 Mb
Release : 2018-09-27
Category : Business & Economics
ISBN : 9789811319815

Get Book

Generalized Preinvexity and Second Order Duality in Multiobjective Programming by Xinmin Yang Pdf

This book introduces readers to several new generalized preinvex functions and generalized invariant monotone functions. It begins by describing the main properties of these functions and various relations. Several examples are then presented to illustrate various interesting relationships among preinvex functions and the properly inclusive relations among the generalized invariant monotonicities. In addition, several second order and higher order symmetric duality models are provided for multi-objective nonlinear programming problems. Lastly, weak and strong duality theorems under generalized convexity assumptions are provided. The book offers a well-synthesized, accessible, and usable treatment for students, researchers and practitioners in the areas of OR, optimization, applied mathematics and engineering, and all those working on a wide range of related problems, which include financial institutions, logistics, transportation, traffic management, etc.

Author : Kazuo Murota
Publisher : SIAM
Page : 411 pages
File Size : 49,9 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 0898718503

Get Book

Discrete Convex Analysis by Kazuo Murota Pdf

Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization. The study of this theory is expanding with the development of efficient algorithms and applications to a number of diverse disciplines like matrix theory, operations research, and economics. This self-contained book is designed to provide a novel insight into optimization on discrete structures and should reveal unexpected links among different disciplines. It is the first and only English-language monograph on the theory and applications of discrete convex analysis.

Author : Peter Bank,Fabrice Baudoin,Hans Föllmer,L. C. G. Rogers,Halil Mete Soner,Nizar Touzi
Publisher : Springer
Page : 178 pages
File Size : 54,7 Mb
Release : 2003-12-15
Category : Mathematics
ISBN : 9783540448594

Get Book

Paris-Princeton Lectures on Mathematical Finance 2002 by Peter Bank,Fabrice Baudoin,Hans Föllmer,L. C. G. Rogers,Halil Mete Soner,Nizar Touzi Pdf

The Paris-Princeton Lectures in Financial Mathematics, of which this is the first volume, will, on an annual basis, publish cutting-edge research in self-contained, expository articles from outstanding - established or upcoming! - specialists. The aim is to produce a series of articles that can serve as an introductory reference for research in the field. It arises as a result of frequent exchanges between the finance and financial mathematics groups in Paris and Princeton. The present volume sets standards with articles by P. Bank/H. Föllmer, F. Baudoin, L.C.G. Rogers, and M. Soner/N. Touzi.

Author : Marco Maggis
Publisher : Ledizioni
Page : 143 pages
File Size : 44,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9788895994598

Get Book

On Quasiconvex Conditional Maps. Duality Results and Applications to Finance by Marco Maggis Pdf

Author : Marina Resta
Publisher : MDPI
Page : 234 pages
File Size : 55,7 Mb
Release : 2020-04-02
Category : Business & Economics
ISBN : 9783039284986

Get Book

Computational Methods for Risk Management in Economics and Finance by Marina Resta Pdf

At present, computational methods have received considerable attention in economics and finance as an alternative to conventional analytical and numerical paradigms. This Special Issue brings together both theoretical and application-oriented contributions, with a focus on the use of computational techniques in finance and economics. Examined topics span on issues at the center of the literature debate, with an eye not only on technical and theoretical aspects but also very practical cases.

Author : M.J. Panik
Publisher : Springer Science & Business Media
Page : 313 pages
File Size : 51,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401581240

Get Book

Fundamentals of Convex Analysis by M.J. Panik Pdf

Fundamentals of Convex Analysis offers an in-depth look at some of the fundamental themes covered within an area of mathematical analysis called convex analysis. In particular, it explores the topics of duality, separation, representation, and resolution. The work is intended for students of economics, management science, engineering, and mathematics who need exposure to the mathematical foundations of matrix games, optimization, and general equilibrium analysis. It is written at the advanced undergraduate to beginning graduate level and the only formal preparation required is some familiarity with set operations and with linear algebra and matrix theory. Fundamentals of Convex Analysis is self-contained in that a brief review of the essentials of these tool areas is provided in Chapter 1. Chapter exercises are also provided. Topics covered include: convex sets and their properties; separation and support theorems; theorems of the alternative; convex cones; dual homogeneous systems; basic solutions and complementary slackness; extreme points and directions; resolution and representation of polyhedra; simplicial topology; and fixed point theorems, among others. A strength of this work is how these topics are developed in a fully integrated fashion.