Author: Darrell Duffie
Publisher:
ISBN:
Category : Hedging (Finance)
Languages : en
Pages : 16

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Book Description

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description
This thesis deals with rational investors who maximize their expected utility in incomplete markets. In Part I, we consider incompleteness induced by jumps and stochastic volatility. Using martingale methods we determine optimal investment strategies for power utility in a wide class of different models. Moreover, we show how first-order approximations of utility-based prices and hedging strategies can be computed by solving a quadratic hedging problem under a suitable measure. This representation result is then applied to affine models leading to semi-explicit solutions. In Part II, we deal with incompleteness due to proportional transaction costs. In finite discrete time we establish that there always exists a shadow price process, which lies within the bid-ask bounds of the original market with transaction costs and leads to the same maximal expected utility. We then show that this idea can also be used in actual computations. This is done by reconsidering the classical Merton problem with transaction costs and solving it by computing the shadow price and the optimal strategy simultaneously.

Author: Srdjan D. Stojanovic
Publisher:
ISBN:
Category :
Languages : en
Pages : 32

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Book Description
By means of the optimal portfolio approach, and in particular by finding what we call the quot;fundamental matrix of derivatives pricing and hedgingquot;, we have formulated a very compact, yet very general form of a Black-Scholes type pricing PDE, and of Black-Scholes type hedging, for any contract in complete or incomplete, multi-factor, multi-tradable, Itocirc;-SDE-setting, under HARA or CARA utility. Our approach to pricing is the one first introduced by Kallsen, called quot;neutral derivative pricingquot;, which assumes that the considered derivative is traded actively. Furthermore, we discuss the relationship between HARA and CARA option pricing theories, and provide an example of a model with stochastic interest rates (in an incomplete market) for which between HARA and CARA (quot;neutralquot;) pricing theories, only HARA theory is possible.

Author: Fwu-Ranq Chang
Publisher: Cambridge University Press
ISBN: 1139452223
Category : Business & Economics
Languages : en
Pages : 346

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Book Description
First published in 2004, this is a rigorous but user-friendly book on the application of stochastic control theory to economics. A distinctive feature of the book is that mathematical concepts are introduced in a language and terminology familiar to graduate students of economics. The standard topics of many mathematics, economics and finance books are illustrated with real examples documented in the economic literature. Moreover, the book emphasises the dos and don'ts of stochastic calculus, cautioning the reader that certain results and intuitions cherished by many economists do not extend to stochastic models. A special chapter (Chapter 5) is devoted to exploring various methods of finding a closed-form representation of the value function of a stochastic control problem, which is essential for ascertaining the optimal policy functions. The book also includes many practice exercises for the reader. Notes and suggested readings are provided at the end of each chapter for more references and possible extensions.

Author: Ioannis Karatzas
Publisher: Springer
ISBN: 1493968459
Category : Mathematics
Languages : en
Pages : 426

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Book Description
This sequel to Brownian Motion and Stochastic Calculus by the same authors develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets, within the context of Brownian-motion-driven asset prices. The latter topic is extended to a study of equilibrium, providing conditions for existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the book. This book will be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.

Author: John R. Birge
Publisher: Elsevier
ISBN: 9780080553252
Category : Business & Economics
Languages : en
Pages : 1026

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Book Description
The remarkable growth of financial markets over the past decades has been accompanied by an equally remarkable explosion in financial engineering, the interdisciplinary field focusing on applications of mathematical and statistical modeling and computational technology to problems in the financial services industry. The goals of financial engineering research are to develop empirically realistic stochastic models describing dynamics of financial risk variables, such as asset prices, foreign exchange rates, and interest rates, and to develop analytical, computational and statistical methods and tools to implement the models and employ them to design and evaluate financial products and processes to manage risk and to meet financial goals. This handbook describes the latest developments in this rapidly evolving field in the areas of modeling and pricing financial derivatives, building models of interest rates and credit risk, pricing and hedging in incomplete markets, risk management, and portfolio optimization. Leading researchers in each of these areas provide their perspective on the state of the art in terms of analysis, computation, and practical relevance. The authors describe essential results to date, fundamental methods and tools, as well as new views of the existing literature, opportunities, and challenges for future research.

Author: Dilip B. Madan
Publisher: Cambridge University Press
ISBN: 100900249X
Category : Mathematics
Languages : en
Pages : 284

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Book Description
What happens to risk as the economic horizon goes to zero and risk is seen as an exposure to a change in state that may occur instantaneously at any time? All activities that have been undertaken statically at a fixed finite horizon can now be reconsidered dynamically at a zero time horizon, with arrival rates at the core of the modeling. This book, aimed at practitioners and researchers in financial risk, delivers the theoretical framework and various applications of the newly established dynamic conic finance theory. The result is a nonlinear non-Gaussian valuation framework for risk management in finance. Risk-free assets disappear and low risk portfolios must pay for their risk reduction with negative expected returns. Hedges may be constructed to enhance value by exploiting risk interactions. Dynamic trading mechanisms are synthesized by machine learning algorithms. Optimal exposures are designed for option positioning simultaneously across all strikes and maturities.

Author: Wendell H. Fleming
Publisher: Springer Science & Business Media
ISBN: 0387310711
Category : Mathematics
Languages : en
Pages : 436

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Book Description
This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.

Author: D. Kannan
Publisher: CRC Press
ISBN: 9780824706609
Category : Mathematics
Languages : en
Pages : 800

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Book Description
An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.

Author: William M. McEneaney
Publisher: Springer Science & Business Media
ISBN: 1461217849
Category : Technology & Engineering
Languages : en
Pages : 660

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Book Description
In view of Professor Wendell Fleming's many fundamental contributions, his profound influence on the mathematical and systems theory communi ties, his service to the profession, and his dedication to mathematics, we have invited a number of leading experts in the fields of control, optimiza tion, and stochastic systems to contribute to this volume in his honor on the occasion of his 70th birthday. These papers focus on various aspects of stochastic analysis, control theory and optimization, and applications. They include authoritative expositions and surveys as well as research papers on recent and important issues. The papers are grouped according to the following four major themes: (1) large deviations, risk sensitive and Hoc control, (2) partial differential equations and viscosity solutions, (3) stochastic control, filtering and parameter esti mation, and (4) mathematical finance and other applications. We express our deep gratitude to all of the authors for their invaluable contributions, and to the referees for their careful and timely reviews. We thank Harold Kushner for having graciously agreed to undertake the task of writing the foreword. Particular thanks go to H. Thomas Banks for his help, advice and suggestions during the entire preparation process, as well as for the generous support of the Center for Research in Scientific Computation. The assistance from the Birkhauser professional staff is also greatly appreciated.