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.

In Part I, the fundamentals of financial thinking and elementary mathematical methods of finance are presented. The method of presentation is simple enough to bridge the elements of financial arithmetic and complex models of financial math developed in the later parts. It covers characteristics of cash flows, yield curves, and valuation of securities. Part II is devoted to the allocation of funds and risk management: classics (Markowitz theory of portfolio), capital asset pricing model, arbitrage pricing theory, asset & liability management, value at risk. The method explanation takes into account the computational aspects. Part III explains modeling aspects of multistage stochastic programming on a relatively accessible level. It includes a survey of existing software, links to parametric, multiobjective and dynamic programming, and to probability and statistics. It focuses on scenario-based problems with the problems of scenario generation and output analysis discussed in detail and illustrated within a case study.

A reprint of one of the classic volumes on portfolio theory and investment, this book has been used by the leading professors at universities such as Stanford, Berkeley, and Carnegie-Mellon. It contains five parts, each with a review of the literature and about 150 pages of computational and review exercises and further in-depth, challenging problems.Frequently referenced and highly usable, the material remains as fresh and relevant for a portfolio theory course as ever.

Recently macroeconomists have intensified their efforts to develop models that are able to generate persistent reactions of real variables to monetary shocks in stochastic DGE models with nominal rigidities. This has proven to be quite difficult in models with price staggering only. Most papers show that output is above steady state only as long as prices are fixed for the firms. In this article particular attention is given to the role of money demand and to the form of the utility function. I consider cash-in-advance- (CIA) as well as money-in-the-utility-function- (MIU) models, with CRRA and GHH preferences, to evaluate their ability to generate persistence. Persistent reactions emerge only with a high value of the elasticity of labor supply with respect to the real wage and an interest rate sensitive money demand function. CIA-models generally create more persistency than MIU-models. In the CIA-setup a CRRA utility function generates more persistence than GHH preferences. The results highlight the importance of the way money is introduced in a New Neoclassical Synthesis model.

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.