The Fundamental Theorem of Asset Pricing Without Probabilistic Prior Assumptions PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download The Fundamental Theorem of Asset Pricing Without Probabilistic Prior Assumptions PDF full book. Access full book title The Fundamental Theorem of Asset Pricing Without Probabilistic Prior Assumptions by Frank Riedel. Download full books in PDF and EPUB format.
Author: Frank Riedel
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
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: Frank Riedel
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
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: Markus Leippold
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
Get Book Here
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: Greg Anderson
Publisher: Springer Nature
ISBN: 3031023994
Category : Mathematics
Languages : en
Pages : 51
Get Book Here
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: Stephen A. Ross
Publisher: Princeton University Press
ISBN: 1400830206
Category : Business & Economics
Languages : en
Pages : 120
Get Book Here
Book Description
Neoclassical Finance provides a concise and powerful account of the underlying principles of modern finance, drawing on a generation of theoretical and empirical advances in the field. Stephen Ross developed the no arbitrage principle, tying asset pricing to the simple proposition that there are no free lunches in financial markets, and jointly with John Cox he developed the related concept of risk-neutral pricing. In this book Ross makes a strong case that these concepts are the fundamental pillars of modern finance and, in particular, of market efficiency. In an efficient market prices reflect the information possessed by the market and, as a consequence, trading schemes using commonly available information to beat the market are doomed to fail. By stark contrast, the currently popular stance offered by behavioral finance, fueled by a number of apparent anomalies in the financial markets, regards market prices as subject to the psychological whims of investors. But without any appeal to psychology, Ross shows that neoclassical theory provides a simple and rich explanation that resolves many of the anomalies on which behavioral finance has been fixated. Based on the inaugural Princeton Lectures in Finance, sponsored by the Bendheim Center for Finance of Princeton University, this elegant book represents a major contribution to the ongoing debate on market efficiency, and serves as a useful primer on the fundamentals of finance for both scholars and practitioners.
Author: Robert A. Jarrow
Publisher: Springer
ISBN: 3319778218
Category : Mathematics
Languages : en
Pages : 457
Get Book Here
Book Description
Yielding new insights into important market phenomena like asset price bubbles and trading constraints, this is the first textbook to present asset pricing theory using the martingale approach (and all of its extensions). Since the 1970s asset pricing theory has been studied, refined, and extended, and many different approaches can be used to present this material. Existing PhD–level books on this topic are aimed at either economics and business school students or mathematics students. While the first mostly ignore much of the research done in mathematical finance, the second emphasizes mathematical finance but does not focus on the topics of most relevance to economics and business school students. These topics are derivatives pricing and hedging (the Black–Scholes–Merton, the Heath–Jarrow–Morton, and the reduced-form credit risk models), multiple-factor models, characterizing systematic risk, portfolio optimization, market efficiency, and equilibrium (capital asset and consumption) pricing models. This book fills this gap, presenting the relevant topics from mathematical finance, but aimed at Economics and Business School students with strong mathematical backgrounds.
Author: Pablo Koch-Medina
Publisher: Springer Nature
ISBN: 3030397246
Category : Mathematics
Languages : en
Pages : 448
Get Book Here
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: Louis Paulot
Publisher:
ISBN:
Category :
Languages : en
Pages : 5
Get Book Here
Book Description
"Fundamental theorem of asset pricing" roughly states that absence of arbitrage opportunity in a market is equivalent to the existence of a risk-neutral probability. We give a simple counterexample to this oversimplified statement. Prices are given by linear forms which do not always correspond to probabilities. We give examples of such cases. We also show that arbitrage freedom is equivalent to the continuity of the pricing linear form in the relevant topology. Finally we analyze the possible loss of martingality of asset prices with lognormal stochastic volatility. For positive correlation martingality is lost when the financial process is modelled through standard probability theory. We show how to recover martingality using the appropriate mathematical tools.
Author: Robert A. Jarrow
Publisher: Springer Nature
ISBN: 3030744108
Category : Business & Economics
Languages : en
Pages : 470
Get Book Here
Book Description
Asset pricing theory yields deep insights into crucial market phenomena such as stock market bubbles. Now in a newly revised and updated edition, this textbook guides the reader through this theory and its applications to markets. The new edition features new results on state dependent preferences, a characterization of market efficiency and a more general presentation of multiple-factor models using only the assumptions of no arbitrage and no dominance. Taking an innovative approach based on martingales, the book presents advanced techniques of mathematical finance in a business and economics context, covering a range of relevant topics such as derivatives pricing and hedging, systematic risk, portfolio optimization, market efficiency, and equilibrium pricing models. For applications to high dimensional statistics and machine learning, new multi-factor models are given. This new edition integrates suicide trading strategies into the understanding of asset price bubbles, greatly enriching the overall presentation and further strengthening the book’s underlying theme of economic bubbles. Written by a leading expert in risk management, Continuous-Time Asset Pricing Theory is the first textbook on asset pricing theory with a martingale approach. Based on the author’s extensive teaching and research experience on the topic, it is particularly well suited for graduate students in business and economics with a strong mathematical background.
Author: Sergio Albeverio
Publisher: Springer Science & Business Media
ISBN: 3540403353
Category : Mathematics
Languages : en
Pages : 294
Get Book Here
Book Description
In World Mathematical Year 2000 the traditional St. Flour Summer School was hosted jointly with the European Mathematical Society. Sergio Albeverio reviews the theory of Dirichlet forms, and gives applications including partial differential equations, stochastic dynamics of quantum systems, quantum fields and the geometry of loop spaces. The second text, by Walter Schachermayer, is an introduction to the basic concepts of mathematical finance, including the Bachelier and Black-Scholes models. The fundamental theorem of asset pricing is discussed in detail. Finally Michel Talagrand, gives an overview of the mean field models for spin glasses. This text is a major contribution towards the proof of certain results from physics, and includes a discussion of the Sherrington-Kirkpatrick and the p-spin interaction models.
Author: Alet Roux
Publisher:
ISBN:
Category :
Languages : en
Pages : 18
Get Book Here
Book Description
We extend the fundamental theorem of asset pricing to a model where the risky stock is subject to proportional transaction costs in the form of bid-ask spreads and the bank account has different interest rates for borrowing and lending. We show that such a model is free of arbitrage if and only if one can embed in it a friction-free model that is itself free of arbitrage, in the sense that there exists an artificial friction-free price for the stock between its bid and ask prices and an artificial interest rate between the borrowing and lending interest rates such that, if one discounts this stock price by this interest rate, then the resulting process is a martingale under some non-degenerate probability measure. Restricting ourselves to the simple case of a finite number of time steps and a finite number of possible outcomes for the stock price, the proof follows by combining classical arguments based on finite-dimensional separation theorems with duality results from linear optimisation.
