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

• 作者: David W. K. Yeung
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Optimal Consumption Uncertain Inter-Temporal BUDGET Stochastic Dynamic Programming Slutsky EQUATION
• 年，卷（期）: 2014,（2）
• 页码范围: 263-284
• 页数: 22页
• 分类号: O1

摘要

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.