Download or read book Minimal Martingale Measure CAPM and Representative Agent Pricing in Incomplete Markets written by Aleš Černý and published by . This book was released on 2020 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: The minimal martingale measure (MMM) was introduced and studied by Fouml;llmer and Schweizer (1990) in the context of mean square hedging in incomplete markets. Recently, the theory of no-good-deal pricing gave further evidence that the MMM plays a prominent role in security valuation in an incomplete market when security prices follow a diffusion process. Namely, it was shown that the price defined by the MMM lies in the centre of no-good-deal price bounds. In the first part of the paper we examine the relationship between the MMM and the optimal portfolio problem in diffusion environment and show that the MMM arises in equilibrium with log-utility maximizing representative agent. A puzzling property of the MMM is that outside the diffusion environment it easily becomes negative. As we show in the second part of the paper this fact can be explained from the link between the MMM and the CAPM risk-neutral measure.

Download or read book Option Pricing In Incomplete Markets Modeling Based On Geometric L evy Processes And Minimal Entropy Martingale Measures written by Yoshio Miyahara and published by World Scientific. This book was released on 2011-11-22 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers the reader practical methods to compute the option prices in the incomplete asset markets. The [GLP & MEMM] pricing models are clearly introduced, and the properties of these models are discussed in great detail. It is shown that the geometric Lévy process (GLP) is a typical example of the incomplete market, and that the MEMM (minimal entropy martingale measure) is an extremely powerful pricing measure.This volume also presents the calibration procedure of the [GLP & MEMM] model that has been widely used in the application of practical problems./a

Download or read book The Minimal Entropy Martingale Measure and Hedging in Incomplete Markets written by Young Lee and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets written by Marco Frittelli and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Let X be a family of stochastic processes on a general filtered probability space (omega,F, F,P). Under the assumption that the set of equivalent martingale measures for X is not empty, we give sufficient conditions for the existence of a unique equivalent martingale measure which minimizes the relative entropy, with respect to P, in the class of martingale measures. We then provide the characterization of the density of the Minimal Entropy Martingale measure, which suggests the equivalence between the maximization of expected exponential utility and the minimization of the relative entropy.

Download or read book Dynamic Asset Pricing Theory written by Darrell Duffie and published by Princeton University Press. This book was released on 2010-01-27 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Minimal Entropy Martingale Measures and the Valuation Problem in Incomplete Markets written by Marco Frittelli and published by . This book was released on 1996 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Optimal Martingale Measure in Continuous Trading Models written by Takuji Arai and published by . This book was released on 2018 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: We discuss the -Optimal Martingale Measure for ∈ (1, ∞) in continuous incomplete markets whose stock price is fluctuated by a -dimensional continuous semimartingale. In this paper, we treat two simple models. One is a model where the mean-variance trade-off process is deterministic. Another is a model where the Minimal Martingale Measure coincides with the Minimal Entropy Martingale Measure. In these models, we prove that the -Optimal Martingale Measure coincides with the Minimal Martingale Measure under some conditions.

Download or read book The Minimal Entropy Martingale Measures and the Valutation Problem in Incomplete Markets written by Marco Frittelli and published by . This book was released on 1996 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Martingale Pricing Measures in Incomplete Markets Via Stochastic Programming Duality in the Dual of L written by Alan J. King and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Agents Agreement and Partial Equilibrium Pricing in Incomplete Markets written by Michail Anthropelos and published by . This book was released on 2008 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider two risk-averse financial agents who negotiate the price of an illiquid indivisible contingent claim in an incomplete semimartingale market environment. Under the assumption that the agents are exponential utility maximizers with non-traded random endowments, we provide necessary and sufficient conditions for the negotiation to be successful, i.e., for the trade to occur. We, also, study the asymptotic case where the size of the claim is small compared to the random endowments and give a full characterization in this case. We, then, study a partial-equilibrium problem for a bundle of divisible claims and establish its existence and uniqueness. A number of technical results on conditional indifference prices are provided. Finally, we generalize the notion of partial-equilibrium pricing in the case where the agents' risk preferences are modelled by convex capital requirements.

Download or read book Quadratic Criteria for Optimal Martingale Measures in Incomplete Markets written by Thomas Andrew McWalter and published by . This book was released on 2006 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Financial Asset Pricing Theory written by Claus Munk and published by Oxford University Press, USA. This book was released on 2013-04-18 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents models for the pricing of financial assets such as stocks, bonds, and options. The models are formulated and analyzed using concepts and techniques from mathematics and probability theory. It presents important classic models and some recent 'state-of-the-art' models that outperform the classics.

Download or read book Equivalent Martingale Measures and Option Princing in Jump Diffusion Markets written by Yury Dranev and published by . This book was released on 2004 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Techniques in Finance written by Ales Cerný and published by Princeton University Press. This book was released on 2009-07-06 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 2003, Mathematical Techniques in Finance has become a standard textbook for master's-level finance courses containing a significant quantitative element while also being suitable for finance PhD students. This fully revised second edition continues to offer a carefully crafted blend of numerical applications and theoretical grounding in economics, finance, and mathematics, and provides plenty of opportunities for students to practice applied mathematics and cutting-edge finance. Ales Cerný mixes tools from calculus, linear algebra, probability theory, numerical mathematics, and programming to analyze in an accessible way some of the most intriguing problems in financial economics. The textbook is the perfect hands-on introduction to asset pricing, optimal portfolio selection, risk measurement, and investment evaluation. The new edition includes the most recent research in the area of incomplete markets and unhedgeable risks, adds a chapter on finite difference methods, and thoroughly updates all bibliographic references. Eighty figures, over seventy examples, twenty-five simple ready-to-run computer programs, and several spreadsheets enhance the learning experience. All computer codes have been rewritten using MATLAB and online supplementary materials have been completely updated. A standard textbook for graduate finance courses Introduction to asset pricing, portfolio selection, risk measurement, and investment evaluation Detailed examples and MATLAB codes integrated throughout the text Exercises and summaries of main points conclude each chapter

Download or read book Optimal Martingale Measures and Hedging in Models Driven by Levy Processes written by Jozef Kollár and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Our research falls into a broad area of pricing and hedging of contingent claims in incomplete markets. In the rst part we introduce the L evy processes as a suitable class of processes for nancial modelling purposes. This in turn causes the market to become incomplete in general and therefore the martingale measure for the pricing/hedging purposes has to be chosen by introducing some subjective criteria. We study several such criteria in the second section for a general stochastic volatility model driven by L evy process, leading to minimal martingale measure, variance-optimal, or the more general q-optimal martingale measure, for which we show the convergence to the minimal entropy martingale measure for q # 1. The martingale measures studied in the second section are put to use in the third section, where we consider various hedging problems in both martingale and semimartingale setting. We study locally risk-minimization hedging problem, meanvariance hedging and the more general p-optimal hedging, of which the meanvariance hedging is a special case for p = 2. Our model allows us to explicitly determine the variance-optimal martingale measure and the mean-variance hedging strategy using the structural results of Gourieroux, Laurent and Pham (1998) extended to discontinuous case by Arai (2005a). Assuming a Markovian framework and appealing to the Feynman-Kac theorem, the optimal hedge can be found by solving a three-dimensional partial integrodi erential equation. We illustrate this in the last section by considering the variance-optimal hedge of the European put option, and nd the solution numerically by applying nite di erence method.

Download or read book Asset Pricing Theory written by Costis Skiadas and published by Princeton University Press. This book was released on 2009-02-09 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asset Pricing Theory is an advanced textbook for doctoral students and researchers that offers a modern introduction to the theoretical and methodological foundations of competitive asset pricing. Costis Skiadas develops in depth the fundamentals of arbitrage pricing, mean-variance analysis, equilibrium pricing, and optimal consumption/portfolio choice in discrete settings, but with emphasis on geometric and martingale methods that facilitate an effortless transition to the more advanced continuous-time theory. Among the book's many innovations are its use of recursive utility as the benchmark representation of dynamic preferences, and an associated theory of equilibrium pricing and optimal portfolio choice that goes beyond the existing literature. Asset Pricing Theory is complete with extensive exercises at the end of every chapter and comprehensive mathematical appendixes, making this book a self-contained resource for graduate students and academic researchers, as well as mathematically sophisticated practitioners seeking a deeper understanding of concepts and methods on which practical models are built. Covers in depth the modern theoretical foundations of competitive asset pricing and consumption/portfolio choice Uses recursive utility as the benchmark preference representation in dynamic settings Sets the foundations for advanced modeling using geometric arguments and martingale methodology Features self-contained mathematical appendixes Includes extensive end-of-chapter exercises

Download or read book Financial Markets and the Real Economy written by John H. Cochrane and published by Now Publishers Inc. This book was released on 2005 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial Markets and the Real Economy reviews the current academic literature on the macroeconomics of finance.