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Shape-preserving dynamic programming

MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2013年第3期77卷 407-421页

作者： Cai, Yongyang Judd, Kenneth L. Stanford Univ Hoover Inst Stanford CA 94305 USA

dynamic programming is the essential tool in dynamic economic analysis. Problems such as portfolio allocation for individuals and optimal growth of national economies are typical examples. numerical methods typically approximate the value function and use value function iteration to compute the value function for the optimal policy. Polynomial approximations are natural choices for approximating value functions when we know that the true value function is smooth. However, numerical value function iteration with polynomial approximations is unstable because standard methods such as interpolation and least squares fitting do not preserve shape. We introduce shape-preserving approximation methods that stabilize value function iteration, and are generally faster than previous stable methods such as piecewise linear interpolation.

关键词： numerical dynamic programming Shape-preserving approximation Multi-stage decision-making problems Value function iteration

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Solving dynamic programming Problems on a Computational Grid

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COMPUTATIONAL ECONOMICS 2015年第2期45卷 261-284页

作者： Cai, Yongyang Judd, Kenneth L. Thain, Greg Wright, Stephen J. Stanford Univ Hoover Inst Stanford CA 94305 USA Univ Chicago Becker Friedman Inst Chicago IL 60637 USA NBER Stanford CA USA Univ Wisconsin Dept Comp Sci Madison WI 53706 USA

We implement a dynamic programming algorithm on a computational grid consisting of loosely coupled processors, possibly including clusters and individual workstations. The grid changes dynamically during the computation, as processors enter and leave the pool of workstations. The algorithm is implemented using the Master-Worker library running on the HTCondor grid computing platform, which can be deployed on many networks. We implement value function iteration for large dynamic programming problems of two kinds: optimal growth problems and dynamic portfolio problems. We present examples that solve in hours on HTCondor but would take weeks if executed on a single workstation. The cost of using HTCondor is small because it uses CPU resources that otherwise would be idle. The use of HTCondor can increase a researcher's computational productivity by at least two orders of magnitude.

关键词： numerical dynamic programming Parallel computing Grid computing Value function iteration dynamic portfolio optimization Multi-country optimal growth

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Continuous state dynamic programming via nonexpansive approximation

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COMPUTATIONAL ECONOMICS 2008年第2期31卷 141-160页

作者： Stachurski, John Kyoto Univ Inst Econ Res Sakyo Ku Kyoto 6068501 Japan

This paper studies fitted value iteration for continuous state numerical dynamic programming using nonexpansive function approximators. A number of approximation schemes are discussed. The main contribution is to prov... 详细信息

关键词： numerical dynamic programming nonexpansive approximation

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Adaptive grids for the estimation of dynamic models

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QME-QUANTITATIVE MARKETING AND ECONOMICS 2022年第2期20卷 179-238页

作者： Lanz, Andreas Reich, Gregor Wilms, Ole HEC Paris Jouy En Josas France Tsumcor Res AG Schwerzenbach Switzerland Univ Hamburg Hamburg Germany Tilburg Univ Tilburg Netherlands

This paper develops a method to flexibly adapt interpolation grids of value function approximations in the estimation of dynamic models using either NFXP (Rust, Econometrica: Journal of the Econometric Society, 55, 999-1033, 1987) or MPEC (Su & Judd, Econometrica: Journal of the Econometric Society, 80, 2213-2230, 2012). Since MPEC requires the grid structure for the value function approximation to be hard-coded into the constraints, one cannot apply iterative node insertion for grid refinement;for NFXP, grid adaption by (iteratively) inserting new grid nodes will generally lead to discontinuous likelihood functions. Therefore, we show how to continuously adapt the grid by moving the nodes, a technique referred to as r-adaption. We demonstrate how to obtain optimal grids based on the balanced error principle, and implement this approach by including additional constraints to the likelihood maximization problem. The method is applied to two models: (i) the bus engine replacement model (Rust, 1987), modified to feature a continuous mileage state, and (ii) to a dynamic model of content consumption using original data from one of the world's leading user-generated content networks in the domain of music.

关键词： numerical dynamic programming Mathematical programming with equilibrium constraints r-adaptive grid refinement Equi-oscillation

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Asymptotic methods for aggregate growth models

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JOURNAL OF ECONOMIC dynamicS & CONTROL 1997年第6期21卷 1025-1042页

作者： Judd, KL Guu, SM HOOVER INST WAR REVOLUT & PEACE STANFORDCA 94305 USA

We use perturbation methods to compute optimal policy functions in simple continuous-and discrete-time aggregate growth models. We demonstrate that computing the kth degree Taylor expansion of the policy function around the steady state involves solving one quadratic equation and k - 1 linear equations. We also compute Pade expansions, and show that both Taylor and Pade expansions can provide excellent solutions far from the steady state.

关键词： perturbation methods numerical dynamic programming

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Intertemporal price discrimination with forward-looking consumers: Application to the US market for console video-games

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QME-QUANTITATIVE MARKETING AND ECONOMICS 2007年第3期5卷 239-292页

作者： Nair, Harikesh Stanford Univ Grad Sch Business Stanford CA 94305 USA

Finns in durable good product markets face incentives to intertemporally price discriminate, by setting high initial prices to sell to consumers with the highest willingness to pay, and cutting prices thereafter to appeal to those with lower willingness to pay. A critical determinant of the profitability of such pricing policies is the extent to which consumers anticipate future price declines, and delay purchases. I develop a framework to investigate empirically the optimal pricing over time of a firm selling a durable-good product to such strategic consumers. Prices in the model are equilibrium outcomes of a game played between forward-looking consumers who strategically delay purchases to avail of lower prices in the future, and a forward-looking firm that takes this consumer behavior into account in formulating its optimal pricing policy. The model outlines first, a dynamic model of demand incorporating forward-looking consumer behavior, and second, an algorithm to compute the optimal dynamic sequence of prices given these demand estimates. The model is solved using numerical dynamic programming techniques. I present an empirical application to the market for video-games in the US. The results indicate that consumer forward-looking behavior has a significant effect on optimal pricing of games in the industry. Simulations reveal that the profit losses of ignoring forward-looking behavior by consumers are large and economically significant, and suggest that market research that provides information regarding the extent of discounting by consumers is valuable to video-game firms.

关键词： durable-good pricing forward-looking consumers Markov-perfect equilibrium numerical dynamic programming video-game industry

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A computational approach to liquidity-constrained firms over an infinite horizon

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JOURNAL OF ECONOMIC dynamicS & CONTROL 2003年第1期28卷 189-205页

作者： Ono, M Fukushima Univ Dept Econ Fukushima 7601296 Japan

This paper examines the behavior of liquidity-constrained firms in a time-series. It illustrates that cash-shortage expectations induce a firm to hold liquid assets, which reveal a nonlinear relationship with the degree of financing constraints. This paper also argues that financial constraints could create serial correlation in a firm's internal funds even if exogenous shocks last for a single period of time. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： business investment economic fluctuations numerical dynamic programming

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dynamic programming with shape-preserving rational spline Hermite interpolation

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ECONOMICS LETTERS 2012年第1期117卷 161-164页

作者： Cai, Yongyang Judd, Kenneth L. Stanford Univ Hoover Inst Stanford CA 94305 USA

numerical methods for dynamic programming often use value function iteration and interpolation. We present a novel shape-preserving rational spline approximation method that improves value function iteration in terms ... 详细信息

关键词： numerical dynamic programming Shape-preserving approximation Hermite interpolation Rational function spline Value function iteration

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Envelope condition method versus endogenous grid method for solving dynamic programming problems

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ECONOMICS LETTERS 2013年第2期120卷 262-266页

作者： Maliar, Lilia Maliar, Serguei Stanford Univ Hoover Inst Stanford CA 94305 USA Univ Alicante Alicante Spain

We introduce an envelope condition method (ECM) for solving dynamic programming problems. The ECM method is simple to implement, dominates conventional value function iteration and is comparable in accuracy and cost t... 详细信息

关键词： numerical dynamic programming Value function iteration Endogenous grid Envelope condition Curse of dimensionality Large scale

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Rational Market Making with Probabilistic Knowledge 12

Rational Market Making with Probabilistic Knowledge

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International Conference on Autonomous Agents and Multiagent Systems

作者： Abraham Othman Tuomas Sandholm Computer Science Department Carnegie Mellon University

ISBN: (纸本)9781627481564

A market maker sets prices over time for wagers that pay out contingent on the future state of the world. The market maker has knowledge of the probability of realizing each state of the world, and of how the price of a bet affects the probability that traders will accept it. We compare the optimal policy for risk-neutral (expected utility maximizing) and Kelly criterion (expected log-utility maximizing) market makers. Computing the optimal policy for a risk-neutral market maker is relatively simple, while computing the optimal policy for a Kelly criterion market maker is challenging, requiring advanced techniques adapted from the computational economics literature to run efficiently. We show that while a risk-neutral market maker has an optimal policy that does not depend on the market maker's state, a Kelly criterion market maker's optimal policy has an intricate dependence on both time and state. Counter-intuitively, a Kelly criterion market maker may offer bets that are myopically irrational with respect to the market maker's beliefs for the entire trading period. In contrast, a risk-neutral market maker never offers a myopically irrational bet.

关键词： Agent Design Computational Economics Interpolation numerical dynamic programming Kelly Criterion Wagering optimal strategy Probability Gambling Prices knowledge

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