This paper analyzes the necessary and sufficient conditions for solving money-in-the-utility-function models when contemporaneous asset returns are uncertain. A unique solution to such models is shown to exist under certain measurability conditions. Stochastic Euler equations, whose existence is normally assumed in these models, are then formally derived. The regularity conditions are weak, and economically innocuous. The results apply to the broad range of discrete-time monetary and financial models that are special cases of the model used in this paper. The method is also applicable to other dynamic models that incorporate contemporaneous uncertainty.
Winner of the prestigious Paul A. Samuelson Award for scholarly writing on lifelong financial security, John Cochrane's Asset Pricing now appears in a revised edition that unifies and brings the science of asset pricing up to date for advanced students and professionals. Cochrane traces the pricing of all assets back to a single idea—price equals expected discounted payoff—that captures the macro-economic risks underlying each security's value. By using a single, stochastic discount factor rather than a separate set of tricks for each asset class, Cochrane builds a unified account of modern asset pricing. He presents applications to stocks, bonds, and options. Each model—consumption based, CAPM, multifactor, term structure, and option pricing—is derived as a different specification of the discounted factor. The discount factor framework also leads to a state-space geometry for mean-variance frontiers and asset pricing models. It puts payoffs in different states of nature on the axes rather than mean and variance of return, leading to a new and conveniently linear geometrical representation of asset pricing ideas. Cochrane approaches empirical work with the Generalized Method of Moments, which studies sample average prices and discounted payoffs to determine whether price does equal expected discounted payoff. He translates between the discount factor, GMM, and state-space language and the beta, mean-variance, and regression language common in empirical work and earlier theory. The book also includes a review of recent empirical work on return predictability, value and other puzzles in the cross section, and equity premium puzzles and their resolution. Written to be a summary for academics and professionals as well as a textbook, this book condenses and advances recent scholarship in financial economics.
Stochastic Optimization Models in Finance focuses on the applications of stochastic optimization models in finance, with emphasis on results and methods that can and have been utilized in the analysis of real financial problems. The discussions are organized around five themes: mathematical tools; qualitative economic results; static portfolio selection models; dynamic models that are reducible to static models; and dynamic models. This volume consists of five parts and begins with an overview of expected utility theory, followed by an analysis of convexity and the Kuhn-Tucker conditions. The reader is then introduced to dynamic programming; stochastic dominance; and measures of risk aversion. Subsequent chapters deal with separation theorems; existence and diversification of optimal portfolio policies; effects of taxes on risk taking; and two-period consumption models and portfolio revision. The book also describes models of optimal capital accumulation and portfolio selection. This monograph will be of value to mathematicians and economists as well as to those interested in economic theory and mathematical economics.
A state-of-the-art introduction to the powerful mathematical and statistical tools used in the field of finance The use of mathematical models and numerical techniques is a practice employed by a growing number of applied mathematicians working on applications in finance. Reflecting this development, Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition bridges the gap between financial theory and computational practice while showing readers how to utilize MATLAB?--the powerful numerical computing environment--for financial applications. The author provides an essential foundation in finance and numerical analysis in addition to background material for students from both engineering and economics perspectives. A wide range of topics is covered, including standard numerical analysis methods, Monte Carlo methods to simulate systems affected by significant uncertainty, and optimization methods to find an optimal set of decisions. Among this book's most outstanding features is the integration of MATLAB?, which helps students and practitioners solve relevant problems in finance, such as portfolio management and derivatives pricing. This tutorial is useful in connecting theory with practice in the application of classical numerical methods and advanced methods, while illustrating underlying algorithmic concepts in concrete terms. Newly featured in the Second Edition: * In-depth treatment of Monte Carlo methods with due attention paid to variance reduction strategies * New appendix on AMPL in order to better illustrate the optimization models in Chapters 11 and 12 * New chapter on binomial and trinomial lattices * Additional treatment of partial differential equations with two space dimensions * Expanded treatment within the chapter on financial theory to provide a more thorough background for engineers not familiar with finance * New coverage of advanced optimization methods and applications later in the text Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition presents basic treatments and more specialized literature, and it also uses algebraic languages, such as AMPL, to connect the pencil-and-paper statement of an optimization model with its solution by a software library. Offering computational practice in both financial engineering and economics fields, this book equips practitioners with the necessary techniques to measure and manage risk.
The ABCs of RBCs is the first book to provide a basic introduction to Real Business Cycle (RBC) and New-Keynesian models. These models argue that random shocks—new inventions, droughts, and wars, in the case of pure RBC models, and monetary and fiscal policy and international investor risk aversion, in more open interpretations—can trigger booms and recessions and can account for much of observed output volatility. George McCandless works through a sequence of these Real Business Cycle and New-Keynesian dynamic stochastic general equilibrium models in fine detail, showing how to solve them, and how to add important extensions to the basic model, such as money, price and wage rigidities, financial markets, and an open economy. The impulse response functions of each new model show how the added feature changes the dynamics. The ABCs of RBCs is designed to teach the economic practitioner or student how to build simple RBC models. Matlab code for solving many of the models is provided, and careful readers should be able to construct, solve, and use their own models. In the tradition of the “freshwater” economic schools of Chicago and Minnesota, McCandless enhances the methods and sophistication of current macroeconomic modeling.
A First Course in Probability with an Emphasis on Stochastic Modeling Probability and Stochastic Modeling not only covers all the topics found in a traditional introductory probability course, but also emphasizes stochastic modeling, including Markov chains, birth-death processes, and reliability models. Unlike most undergraduate-level probability texts, the book also focuses on increasingly important areas, such as martingales, classification of dependency structures, and risk evaluation. Numerous examples, exercises, and models using real-world data demonstrate the practical possibilities and restrictions of different approaches and help students grasp general concepts and theoretical results. The text is suitable for majors in mathematics and statistics as well as majors in computer science, economics, finance, and physics. The author offers two explicit options to teaching the material, which is reflected in "routes" designated by special "roadside" markers. The first route contains basic, self-contained material for a one-semester course. The second provides a more complete exposition for a two-semester course or self-study.
The underlying theme of this volume is how to invest assets over time to achieve satisfactory returns subject to uncertainties, various constraints and liability commitments. Most investors, be they individuals or institutions, do not diversify properly across markets nor across time. The papers utilize several approaches and integrate a number of techniques as well as discussing a variety of models that have either been implemented, are close to being implemented, or represent new innovative approaches that may lead to future novel applications. Other issues address the future of asset-liability management modeling. This includes models for individuals, and various financial institutions such as banks and insurance companies. This will lead to custom products, that is, financial engineering. All in all, this will be essential reading for all involved in analysing the financial markets.
Empirical evidence on money, prices, and output -- Money-in-the-utility function -- Money and transactions -- Money and public finance -- Money in the short run : informational and portfolio rigidities -- Money in the short run : nominal price and wage rigidities -- Discretionary policy and time inconsistency -- New keynesian monetary economics -- Money and the open economy -- Financial markets and monetary policy -- Monetary policy and operating procedures.
