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Geometric Asymptotic Approximation of Value Functions

  • Axel Anderson
Veröffentlicht/Copyright: 10. Dezember 2009
The B.E. Journal of Theoretical Economics
Aus der Zeitschrift The B.E. Journal of Theoretical Economics Band 9 Heft 1

This paper characterizes the behavior of value functions in dynamic stochastic discounted programming models near fixed points of the state space. When the second derivative of the flow payoff function is bounded, the value function is proportional to a linear function plus geometric term. A specific formula for the exponent of this geometric term is provided. This exponent continuously falls in the rate of patience.If the state variable is a martingale, the second derivative of the value function is unbounded. If the state variable is instead a strict local submartingale, then the same holds for the first derivative of the value function. Thus, the proposed approximation is more accurate than Taylor series approximation.The approximation result is used to characterize locally optimal policies in several fundamental economic problems.

Keywords: stochastic dynamic programming; value function approximation; learning
Published Online: 2009-12-10

©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston

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  3. Satisficing: A 'Pretty Good' Heuristic
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  9. Competition May Reduce the Revenue in a First Price Auction with Affiliated Private Values
  10. Topics Article
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  12. Why (and When) are Preferences Convex? Threshold Effects and Uncertain Quality
  13. A Two-Step Subsidy Scheme to Overcome Network Externalities in a Dynamic Game
  14. Oligopolistic Certification
  15. Envy-Free and Efficient Minimal Rights: Recursive No-Envy
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  17. Inflation, Self Insurance and the Friedman Rule in Economies with Uninsurable Idiosyncratic Risks
  18. Advertising and Cost Reduction
  19. Directed Search, Rationing and Wage Dispersion
  20. Optimism and Bargaining Inefficiency
  21. Fair Depreciation: A Shapley Value Approach
  22. Product Variety, Scale Economies, and Environmental Taxes
  23. Market Competition and Lower Tier Incentives
  24. Vertical Differentiation, Social Networks and Compatibility Decisions
  25. Asymmetric Bertrand-Edgeworth Oligopoly and Mergers
  26. Consumer Rationing and the Cournot Outcome
  27. Representations and Identities for Homogeneous Technologies
  28. Monitoring Gains and Decentralization
  29. Cross-Cultural Trade and Institutional Stability
  30. Universal Service Obligations and Competition with Asymmetric Information
  31. A Duopoly Model of Political Agency with Applications to Anti-Corruption Reform
  32. Simple Economies with Multiple Equilibria
  33. A Note on Herbert Gintis' "Emergence of a Price System from Decentralized Bilateral Exchange"
  34. Contributions Article
  35. Continuous Preferences and Discontinuous Choices: How Altruists Respond to Incentives
  36. Reputation, Career Concerns, and Job Assignments
  37. Fluctuations in Overlapping Generations Economies
  38. Principal and Expert Agent
  39. Sale of a Deteriorating Asset via Sequential Search
  40. The Efficiency of Observability and Mutual Linkage
  41. A Positive Theory of Income Taxation
  42. Supply Theory sans Profit Maximization
  43. The Dynamics of Collective Reputation
  44. Identifying Community Structures from Network Data via Maximum Likelihood Methods
  45. Income Distribution, Market Structure, and Individual Welfare
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  47. Geometric Asymptotic Approximation of Value Functions
  48. Sequential Auctions with Multi-Unit Demands
https://doi.org/10.2202/1935-1704.1532
Schlagwörter für diesen Artikel
stochastic dynamic programming; value function approximation; learning

Artikel in diesem Heft

  1. Advances Article
  2. Private Information of Nonpaternalistic Altruism: Exaggeration and Reciprocation of Generosity
  3. Satisficing: A 'Pretty Good' Heuristic
  4. Optimal Auctions with Simultaneous and Costly Participation
  5. Temptations in General Settings
  6. Learning in Bayesian Games with Binary Actions
  7. Contracting in the Presence of Judicial Agency
  8. Updating Ambiguity Averse Preferences
  9. Competition May Reduce the Revenue in a First Price Auction with Affiliated Private Values
  10. Topics Article
  11. Incentive Schemes in Peer-to-Peer Networks
  12. Why (and When) are Preferences Convex? Threshold Effects and Uncertain Quality
  13. A Two-Step Subsidy Scheme to Overcome Network Externalities in a Dynamic Game
  14. Oligopolistic Certification
  15. Envy-Free and Efficient Minimal Rights: Recursive No-Envy
  16. Risk Premiums versus Waiting-Options Premiums: A Simple Numerical Example
  17. Inflation, Self Insurance and the Friedman Rule in Economies with Uninsurable Idiosyncratic Risks
  18. Advertising and Cost Reduction
  19. Directed Search, Rationing and Wage Dispersion
  20. Optimism and Bargaining Inefficiency
  21. Fair Depreciation: A Shapley Value Approach
  22. Product Variety, Scale Economies, and Environmental Taxes
  23. Market Competition and Lower Tier Incentives
  24. Vertical Differentiation, Social Networks and Compatibility Decisions
  25. Asymmetric Bertrand-Edgeworth Oligopoly and Mergers
  26. Consumer Rationing and the Cournot Outcome
  27. Representations and Identities for Homogeneous Technologies
  28. Monitoring Gains and Decentralization
  29. Cross-Cultural Trade and Institutional Stability
  30. Universal Service Obligations and Competition with Asymmetric Information
  31. A Duopoly Model of Political Agency with Applications to Anti-Corruption Reform
  32. Simple Economies with Multiple Equilibria
  33. A Note on Herbert Gintis' "Emergence of a Price System from Decentralized Bilateral Exchange"
  34. Contributions Article
  35. Continuous Preferences and Discontinuous Choices: How Altruists Respond to Incentives
  36. Reputation, Career Concerns, and Job Assignments
  37. Fluctuations in Overlapping Generations Economies
  38. Principal and Expert Agent
  39. Sale of a Deteriorating Asset via Sequential Search
  40. The Efficiency of Observability and Mutual Linkage
  41. A Positive Theory of Income Taxation
  42. Supply Theory sans Profit Maximization
  43. The Dynamics of Collective Reputation
  44. Identifying Community Structures from Network Data via Maximum Likelihood Methods
  45. Income Distribution, Market Structure, and Individual Welfare
  46. Free Riding in Combinatorial First-Price Sealed-Bid Auctions
  47. Geometric Asymptotic Approximation of Value Functions
  48. Sequential Auctions with Multi-Unit Demands
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