Options
Optimal consumption under uncertainties: Random horizon stochastic dynamic Roy's identity and Slutsky equation
Author(s)
Date Issued
2014
Journal
Citation
Applied Mathematics, Jan 2014, vol. 5(2), pp. 263-284.
Type
Peer Reviewed Journal Article
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.
Availability at HKSYU Library
