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Optimal Consumption over Time when Prices and Interest Rates Follow a Markovian Process
A. Anastasopoulos
Stratis Kounias
Abstract
This paper is a study on optimal consumption over time under the assumption of uncertainty about prices and interest rates. A stochastic model has been developed in which present wealth is either consumed or invested in a future commodity and loans. The possibility of lending and borrowing allows the model to capture some of the aspects of a monetary economy, such as the effects of actual or anticipated inflation on optimal plans. Future prices follow a Markovian process. Conditions for the existence of optimal policies are given for concave utility functions in general, but constant elasticity utility functions are studied in greater detail. The case in which the expected value of the discounted stream of utilities is infinite, is also investigated.
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