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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.
Imagine you are about to play a repeated strategic-form game against a randomly selected Stanford MBA student. You may not talk to her before or during the play of the game - interactions are computer-mediated. To the extent that it matters, her exposure to game theory has consisted of two lectures in the autumn quarter of her first year (which prominently featured an informal account of the folk theorem, based on the prisoners' dilemma); subsequently, she has specialized in courses in finance and accounting.
The game is played repeatedly, with a constant termination probability: You play once and learn (to an extent specified below) the outcome of the first round of play. Then a two-digit random number is drawn: If it is 00, the interaction is over; anything else and you play again. Hence after each round there is a 0.01 chance of the interaction ending and a 0.99 chance of it going on for at least one more round.
The stakes per round are on the order of tens of dollars, enough (I hope) so you and she will take the game seriously, but not so large that risk aversion or liquidity constraints play an appreciable role. Your name and hers will be shielded so that reputation effects (outside of this encounter) can be ignored.