This book examines whether continuous-time models in frictionless financial economies can be well approximated by discrete-time models. It specifically looks to answer the question: in what sense and to what extent does the famous Black-Scholes-Merton (BSM) continuous-time model of financial markets idealize more realistic discrete-time models of those markets? While it is well known that the BSM model is an idealization of discrete-time economies where the stock price process is driven by a binomial random walk, it is less known that the BSM model idealizes discrete-time economies whose stock price process is driven by more general random walks. Starting with the basic foundations of discrete-time and continuous-time models, David M. Kreps takes the reader through to this important insight with the goal of lowering the entry barrier for many mainstream financial economists, thus bringing less-technical readers to a better understanding of the connections between BSM and nearby discrete-economies.

"I began this monograph (which, at the time, was a nascent paper) with the objective of understandinghow and how well continuous-time models of economic phenomena - and in particular models that employ Brownian motion - relate to "near by" discrete-time models. We know by examples that the connections are sometimes not altogether obvious; see, for instance, Fudenberg and Levine (2009) and Sadzik and Stacchetti (2015). So, it seemed to me, a general theory connecting the two types of models ought to be available"--

A comprehensive introduction of fundamental panel data methodologies.

Stochastic Finance provides an introduction to mathematical finance that is unparalleled in its accessibility. Through classroom testing, the authors have identified common pain points for students, and their approach takes great care to help the reader to overcome these difficulties and to foster understanding where comparable texts often do not. Written for advanced undergraduate students, and making use of numerous detailed examples to illustrate key concepts, this text provides all the mathematical foundations necessary to model transactions in the world of finance. A first course in probability is the only necessary background. The book begins with the discrete binomial model and the finite market model, followed by the continuous Black–Scholes model. It studies the pricing of European options by combining financial concepts such as arbitrage and self-financing trading strategies with probabilistic tools such as sigma algebras, martingales and stochastic integration. All these concepts are introduced in a relaxed and user-friendly fashion.

This book brings together the author's pioneering work, written over the last twenty years, on the use of differential methods in general equilibrium theory.

Master the essential mathematical tools required for option pricing within the context of a specific, yet fundamental, pricing model.

The theory of revealed preference has a long, distinguished tradition in economics but lacked a systematic presentation of the theory until now. This book deals with basic questions in economic theory and studies situations in which empirical observations are consistent or inconsistent with some of the best known economic theories.