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

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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

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