Dynamic programming for non-additive stochastic objectives

Dynamic programming for non-additive stochastic objectives

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Article ID: iaor1999907
Country: United States
Volume: 25
Issue: 4
Start Page Number: 391
End Page Number: 442
Publication Date: Oct 1996
Journal: Journal of Mathematical Economics
Authors: ,
Abstract:

We derive the existence of an optimum and the techniques of dynamic programming for non-additive stochastic objectives. Our key assumption for non-negative objectives is that asymptotic impatience exceeds asymptotic ‘mean’ growth, where ‘mean’ growth is derived not only from intertemporal inelasticity and the random return on investment but also from the curvature of the non-additive stochastic aggregator (i.e. the ‘certainty equivalent’). We provide broad families of new, interesting, and tractable examples. They illustrate that ‘mean’ growth can exist even when the distribution of returns has unbounded support, that power discounting often implies infinite asymptotic impatience, and that non-positive objectives are easily handled with few restrictions on growth.

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