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D. P. Bertsekas and S. E. Shreve, “Stochastic Optimal Control: The Discrete-Time Case,” Athena Scientific, 1996.

has been cited by the following article:

• TITLE: Optimal Consumption under Uncertainties: Random Horizon Stochastic Dynamic Roy’s Identity and Slutsky Equation

  AUTHORS: David W. K. Yeung

  KEYWORDS: Optimal Consumption; Uncertain Inter-Temporal Budget; Stochastic Dynamic Programming; Slutsky Equation

  JOURNAL NAME: Applied Mathematics, Vol.5 No.2, January 20, 2014

  ABSTRACT: This paper extends Slutsky’s classic work on consumer theory to a random horizon stochastic dynamic framework in which the consumer has an inter-temporal planning horizon with uncertainties in future incomes and life span. Utility maximization leading to a set of ordinary wealth-dependent demand functions is performed. A dual problem is set up to derive the wealth compensated demand functions. This represents the first time that wealth-dependent ordinary demand functions and wealth compensated demand functions are obtained under these uncertainties. The corresponding Roy’s identity relationships and a set of random horizon stochastic dynamic Slutsky equations are then derived. The extension incorporates realistic characteristics in consumer theory and advances the conventional microeconomic study on consumption to a more realistic optimal control framework.