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Author: Winslow Carter Strong Publisher: ISBN: 9781124885995 Category : Languages : en Pages : 155
Book Description
The topic motivating this dissertation is functionally generated portfolios and their capacity to deliver relative arbitrage, an aspect of stochastic portfolio theory (SPT). The aim is to relax some of the common assumptions of SPT and explore the performance of functionally generated portfolios in this more general setting, with an eye towards arbitrage. In particular, the assumption of a constant number of companies in the market model is relaxed, as well as the assumption that all changes in capitalizations are passed on as returns to investors through the stochastic integral.
Author: Winslow Carter Strong Publisher: ISBN: 9781124885995 Category : Languages : en Pages : 155
Book Description
The topic motivating this dissertation is functionally generated portfolios and their capacity to deliver relative arbitrage, an aspect of stochastic portfolio theory (SPT). The aim is to relax some of the common assumptions of SPT and explore the performance of functionally generated portfolios in this more general setting, with an eye towards arbitrage. In particular, the assumption of a constant number of companies in the market model is relaxed, as well as the assumption that all changes in capitalizations are passed on as returns to investors through the stochastic integral.
Author: E. Robert Fernholz Publisher: Springer Science & Business Media ISBN: 1475736991 Category : Business & Economics Languages : en Pages : 190
Book Description
Stochastic portfolio theory is a mathematical methodology for constructing stock portfolios and for analyzing the effects induced on the behavior of these portfolios by changes in the distribution of capital in the market. Stochastic portfolio theory has both theoretical and practical applications: as a theoretical tool it can be used to construct examples of theoretical portfolios with specified characteristics and to determine the distributional component of portfolio return. This book is an introduction to stochastic portfolio theory for investment professionals and for students of mathematical finance. Each chapter includes a number of problems of varying levels of difficulty and a brief summary of the principal results of the chapter, without proofs.
Author: Tomas Björk Publisher: ISBN: 0191525103 Category : Arbitrage Languages : en Pages : 325
Book Description
This text provides an accessible introduction to the classical mathematical underpinnings of modern finance. Professor Bjork concentrates on the probabilistic theory of continuous arbitrage pricing of financial derivatives.
Author: Fred Espen Benth Publisher: Springer Science & Business Media ISBN: 9783540405023 Category : Business & Economics Languages : en Pages : 180
Book Description
This is a very basic and accessible introduction to option pricing, invoking a minimum of stochastic analysis and requiring only basic mathematical skills. It covers the theory essential to the statistical modeling of stocks, pricing of derivatives with martingale theory, and computational finance including both finite-difference and Monte Carlo methods.
Author: Ioannis Karatzas Publisher: American Mathematical Soc. ISBN: 1470465981 Category : Education Languages : en Pages : 309
Book Description
This book develops a mathematical theory for finance, based on a simple and intuitive absence-of-arbitrage principle. This posits that it should not be possible to fund a non-trivial liability, starting with initial capital arbitrarily near zero. The principle is easy-to-test in specific models, as it is described in terms of the underlying market characteristics; it is shown to be equivalent to the existence of the so-called “Kelly” or growth-optimal portfolio, of the log-optimal portfolio, and of appropriate local martingale deflators. The resulting theory is powerful enough to treat in great generality the fundamental questions of hedging, valuation, and portfolio optimization. The book contains a considerable amount of new research and results, as well as a significant number of exercises. It can be used as a basic text for graduate courses in Probability and Stochastic Analysis, and in Mathematical Finance. No prior familiarity with finance is required, but it is assumed that readers have a good working knowledge of real analysis, measure theory, and of basic probability theory. Familiarity with stochastic analysis is also assumed, as is integration with respect to continuous semimartingales.
Author: Jorge Guijarro Ordonez Publisher: ISBN: Category : Languages : en Pages :
Book Description
The central problem of this dissertation is the mathematical study of statistical arbitrage in the case of a high-dimensional number of assets, which is analyzed from two complementary approaches. In the first part of the dissertation, we consider the problem from a stochastic control perspective that extends and combines the Avellaneda and Lee model for statistical arbitrage with the classical Merton framework for portfolio theory. In our framework, given a high-dimensional number of assets and a mean-reverting stochastic model for the dynamics of their residuals through a statistical factor model, an investor must decide how to trade the original assets to maximize the expected utility of her terminal wealth in a finite time horizon, while taking into account market frictions and common statistical arbitrage constraints like dollar neutrality. We study continuous-time and discrete-time versions of the trading problem with both exponential utility and a mean-variance objective, and we prove the existence of interpretable analytic or semi-analytic optimal trading strategies through the study of the corresponding Hamilton-Jacobi-Bellman partial differential equations. We supplement this theoretical study with extensive Monte Carlo simulations that provide further insight about the qualitative behavior of the found optimal strategies under different parameter regimes. In the second part of the dissertation, we complement the previous study with a general deep-learning framework that mitigates two limitations of the stochastic control approach: strong modeling assumptions on the residual dynamics, and solving the high-dimensional Hamilton-Jacobi-Bellman equations for more realistic objective functions, models, and constraints. To this end, we frame the residual modeling and trading problems as a double optimal control problem, that we solve numerically by restricting the controls to a series of functional classes that range from classical parametric models to the most advanced neural network architectures adapted to our problem. We test these methods by conducting an extensive out-of-sample empirical study with high-capitalization U.S. equity data over the main families of factor models, which provides a comprehensive analysis of the importance of the different elements of a statistical arbitrage strategy and the gains from machine learning methods.
Author: Pablo Koch-Medina Publisher: Springer Nature ISBN: 3030397246 Category : Mathematics Languages : en Pages : 448
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: Jack Clark Francis Publisher: John Wiley & Sons ISBN: 111837052X Category : Business & Economics Languages : en Pages : 576
Book Description
A through guide covering Modern Portfolio Theory as well as the recent developments surrounding it Modern portfolio theory (MPT), which originated with Harry Markowitz's seminal paper "Portfolio Selection" in 1952, has stood the test of time and continues to be the intellectual foundation for real-world portfolio management. This book presents a comprehensive picture of MPT in a manner that can be effectively used by financial practitioners and understood by students. Modern Portfolio Theory provides a summary of the important findings from all of the financial research done since MPT was created and presents all the MPT formulas and models using one consistent set of mathematical symbols. Opening with an informative introduction to the concepts of probability and utility theory, it quickly moves on to discuss Markowitz's seminal work on the topic with a thorough explanation of the underlying mathematics. Analyzes portfolios of all sizes and types, shows how the advanced findings and formulas are derived, and offers a concise and comprehensive review of MPT literature Addresses logical extensions to Markowitz's work, including the Capital Asset Pricing Model, Arbitrage Pricing Theory, portfolio ranking models, and performance attribution Considers stock market developments like decimalization, high frequency trading, and algorithmic trading, and reveals how they align with MPT Companion Website contains Excel spreadsheets that allow you to compute and graph Markowitz efficient frontiers with riskless and risky assets If you want to gain a complete understanding of modern portfolio theory this is the book you need to read.
Author: Peter Bossaerts Publisher: ISBN: Category : Languages : en Pages : 41
Book Description
In one of the early attempts to model stochastic volatility, Clark [1973] conjectured that the size of asset price movements is tied to the rate at which transactions occur. To formally analyze the econometric implications, he distinguished between transaction time and calendar time. The present paper exploits Clark's strategy for a different purpose, namely, asset pricing. It studies arbitrage-based pricing in economies where: (i)trade takes place in transaction time, (ii) there is a single state variable whose transaction-time price path is binomial, (iii) there are riskfree bonds with calendar-time maturities, and (iv) the relation between transaction time and calendar time is stochastic. The state variable could be interpreted in various ways. E.g., it could be the price of a share of stock, as in Black and Scholes [1973], or a factor that summarizes changes in the investment opportunity set, as in Cox, Ingersoll and Ross [1985] or one that drives changes in the term structure of interest rates (Ho and Lee [1986], Heath, Jarrow and Morton [1992]). Property (iv) generally introduces stochastic volatility in the process of the state variable when recorded in calendar time.The paper investigates the pricing of derivative securities with calendar-time maturities. The restrictions obtained in Merton [1973] using simple buy-and-hold arbitrage portfolio arguments do not necessarily obtain. Conditions are derived for all derivatives to be priced by dynamic arbitrage, i.e., for market completeness in the sense of Harrison and Pliska [1981]. A particular class of stationary economies where markets are indeed complete is characterized.
Author: Winslow Carter Strong
Author: Winslow Carter Strong
Author: E. Robert Fernholz
Author: Tomas Björk
Author: Fred Espen Benth
Author: Ioannis Karatzas
Author: Jorge Guijarro Ordonez
Author: Andrey M. Lizyayev
Author: Pablo Koch-Medina
Author: Jack Clark Francis
Author: Peter Bossaerts