Fundamental Theorem of Asset Pricing on Measurable Spaces Under Uncertainty PDF Download
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Author: Markus Leippold
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
It is common in the financial mathematics literature to start by fixing a probability space $( Omega, mathcal F, mathbb P)$, on which the underlying price process is defined. We depart from this route in that we do not fix the prior $ mathbb P$. Under very general assumptions, we recover the Fundamental Theorem of Asset Pricing in discrete time under either a multiple-priors or a prior-free setting. We only require that $( Omega, mathcal F)$ is a measurable space, while the multiple priors can be non-equivalent. Furthermore, the initial price of our market model does not need to be constant, but only measurable.
Author: Markus Leippold
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
It is common in the financial mathematics literature to start by fixing a probability space $( Omega, mathcal F, mathbb P)$, on which the underlying price process is defined. We depart from this route in that we do not fix the prior $ mathbb P$. Under very general assumptions, we recover the Fundamental Theorem of Asset Pricing in discrete time under either a multiple-priors or a prior-free setting. We only require that $( Omega, mathcal F)$ is a measurable space, while the multiple priors can be non-equivalent. Furthermore, the initial price of our market model does not need to be constant, but only measurable.
Author: Erhan Bayraktar
Publisher:
ISBN:
Category :
Languages : en
Pages : 24
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Book Description
We prove the Fundamental Theorem of Asset Pricing for a discrete time financial market where trading is subject to proportional transaction cost and the asset price dynamic is modeled by a family of probability measures, possibly non-dominated.Using a backward-forward scheme, we show that when the market consists of a money market account and a single stock, no-arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of consistent price systems. We also show that when the market consists of multiple dynamically traded assets and satisfies efficient friction, strict no-arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of strictly consistent price systems.
Author: Frank Riedel
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Motivated by recent discussions on Knightian uncertainty, we develop the fundamental theorem of asset pricing in a probability-free setup. The usual assumption of a prior probability is removed; a certain continuity property in the state variable is introduced instead. We show that one can still develop a meaningful and rich theory of asset pricing. The pricing functional given by an arbitrage-free market can be identified with a full support martingale measure (instead of equivalent martingale measure). We relate the no arbitrage theory to economic equilibrium by establishing a variant of the Harrison-Kreps-Theorem on viability and no arbitrage. Finally, we consider (super)hedging of contingent claims and embed it in a classical infinite-dimensional linear programming problem.
Author: Greg Anderson
Publisher: Morgan & Claypool Publishers
ISBN: 1608454967
Category : Technology & Engineering
Languages : en
Pages : 63
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Book Description
This is a short book on the fundamental concepts of the no-arbitrage theory of pricing financial derivatives. Its scope is limited to the general discrete setting of models for which the set of possible states is finite and so is the set of possible trading times--this includes the popular binomial tree model. This setting has the advantage of being fairly general while not requiring a sophisticated understanding of analysis at the graduate level. Topics include understanding the several variants of "arbitrage", the fundamental theorems of asset pricing in terms of martingale measures, and applications to forwards and futures. The authors' motivation is to present the material in a way that clarifies as much as possible why the often confusing basic facts are true. Therefore the ideas are organized from a mathematical point of view with the emphasis on understanding exactly what is under the hood and how it works. Every effort is made to include complete explanations and proofs, and the reader is encouraged to work through the exercises throughout the book. The intended audience is students and other readers who have an undergraduate background in mathematics, including exposure to linear algebra, some advanced calculus, and basic probability. The book has been used in earlier forms with students in the MS program in Financial Mathematics at Florida State University, and is a suitable text for students at that level. Students who seek a second look at these topics may also find this book useful. Table of Contents: Overture: Single-Period Models / The General Discrete Model / The Fundamental Theorems of Asset Pricing / Forwards and Futures / Incomplete Markets
Author: Meriton Ibraimi
Publisher:
ISBN:
Category :
Languages : en
Pages : 25
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Book Description
The classical version of the Fundamental Theorem of Asset Pricing requires that zero-sets of the real-world probability measure P are known. We chose a different route and start from a possibly non-dominated set of probability measures P representing uncertainty about the zero-sets of the real world measure. Since the concept of equivalence of measures becomes meaningless under such a framework, we use the notion of P-full support, which is a condition on the support of a martingale measure Q. We derive a version of the Fundamental Theorem of Asset Pricing and find that no-arbitrage, in our context, is equivalent to the existence of a discrete martingale measure.
Author: Erhan Bayraktar
Publisher:
ISBN:
Category :
Languages : en
Pages : 9
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Book Description
We show that the results of the Fundamental Theorem of Asset Pricing and the super-hedging theorem can be extended to the case in which the options available for static hedging (hedging options) are quoted with bid-ask spreads. In this set-up, we need to work with the notion of robust no-arbitrage which turns out to be equivalent to no-arbitrage under the additional assumption that hedging options with non-zero spread are non-redundant. A key result is the closedness of the set of attainable claims, which requires a new proof in our setting.
Author: Pablo Koch-Medina
Publisher: Springer Nature
ISBN: 3030397246
Category : Mathematics
Languages : en
Pages : 448
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Book Description
Arbitrage Theory provides the foundation for the pricing of financial derivatives and has become indispensable in both financial theory and financial practice. This textbook offers a rigorous and comprehensive introduction to the mathematics of arbitrage pricing in a discrete-time, finite-state economy in which a finite number of securities are traded. In a first step, various versions of the Fundamental Theorem of Asset Pricing, i.e., characterizations of when a market does not admit arbitrage opportunities, are proved. The book then focuses on incomplete markets where the main concern is to obtain a precise description of the set of “market-consistent” prices for nontraded financial contracts, i.e. the set of prices at which such contracts could be transacted between rational agents. Both European-type and American-type contracts are considered. A distinguishing feature of this book is its emphasis on market-consistent prices and a systematic description of pricing rules, also at intermediate dates. The benefits of this approach are most evident in the treatment of American options, which is novel in terms of both the presentation and the scope, while also presenting new results. The focus on discrete-time, finite-state models makes it possible to cover all relevant topics while requiring only a moderate mathematical background on the part of the reader. The book will appeal to mathematical finance and financial economics students seeking an elementary but rigorous introduction to the subject; mathematics and physics students looking for an opportunity to get acquainted with a modern applied topic; and mathematicians, physicists and quantitatively inclined economists working or planning to work in the financial industry.
Author: Darrell Duffie
Publisher: Princeton University Press
ISBN: 1400829208
Category : Business & Economics
Languages : en
Pages : 488
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Book Description
This is a thoroughly updated edition of Dynamic Asset Pricing Theory, the standard text for doctoral students and researchers on the theory of asset pricing and portfolio selection in multiperiod settings under uncertainty. The asset pricing results are based on the three increasingly restrictive assumptions: absence of arbitrage, single-agent optimality, and equilibrium. These results are unified with two key concepts, state prices and martingales. Technicalities are given relatively little emphasis, so as to draw connections between these concepts and to make plain the similarities between discrete and continuous-time models. Readers will be particularly intrigued by this latest edition's most significant new feature: a chapter on corporate securities that offers alternative approaches to the valuation of corporate debt. Also, while much of the continuous-time portion of the theory is based on Brownian motion, this third edition introduces jumps--for example, those associated with Poisson arrivals--in order to accommodate surprise events such as bond defaults. Applications include term-structure models, derivative valuation, and hedging methods. Numerical methods covered include Monte Carlo simulation and finite-difference solutions for partial differential equations. Each chapter provides extensive problem exercises and notes to the literature. A system of appendixes reviews the necessary mathematical concepts. And references have been updated throughout. With this new edition, Dynamic Asset Pricing Theory remains at the head of the field.
Author: Bing Cheng
Publisher: World Scientific
ISBN: 9812832505
Category : Business & Economics
Languages : en
Pages : 91
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Book Description
Modern asset pricing models play a central role in finance and economic theory and applications. This book introduces a structural theory to evaluate these asset pricing models and throws light on the existence of Equity Premium Puzzle. Based on the structural theory, some algebraic (valuation-preserving) operations are developed in asset spaces and pricing kernel spaces. This has a very important implication leading to practical guidance in portfolio management and asset allocation in the global financial industry. The book also covers topics, such as the role of over-confidence in asset pricing modeling, relationship of the portfolio insurance with option and consumption-based asset pricing models, etc.
Author: T. Kariya
Publisher: Springer Science & Business Media
ISBN: 1441992308
Category : Business & Economics
Languages : en
Pages : 273
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Book Description
1. Main Goals The theory of asset pricing has grown markedly more sophisticated in the last two decades, with the application of powerful mathematical tools such as probability theory, stochastic processes and numerical analysis. The main goal of this book is to provide a systematic exposition, with practical appli cations, of the no-arbitrage theory for asset pricing in financial engineering in the framework of a discrete time approach. The book should also serve well as a textbook on financial asset pricing. It should be accessible to a broad audi ence, in particular to practitioners in financial and related industries, as well as to students in MBA or graduate/advanced undergraduate programs in finance, financial engineering, financial econometrics, or financial information science. The no-arbitrage asset pricing theory is based on the simple and well ac cepted principle that financial asset prices are instantly adjusted at each mo ment in time in order not to allow an arbitrage opportunity. Here an arbitrage opportunity is an opportunity to have a portfolio of value aat an initial time lead to a positive terminal value with probability 1 (equivalently, at no risk), with money neither added nor subtracted from the portfolio in rebalancing dur ing the investment period. It is necessary for a portfolio of valueato include a short-sell position as well as a long-buy position of some assets.
