Dynamic programming for non-additive stochastic objectives

Hiroyuki Ozaki, Peter A. Streufert

Research output: Contribution to journalArticle

15 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)391-442
Number of pages52
JournalJournal of Mathematical Economics
Volume25
Issue number4
DOIs
Publication statusPublished - 1996

Keywords

  • Aggregator
  • Certainty equivalent
  • Dynamic programming
  • Growthi
  • Impatience
  • Non-additive stochastic objectives

ASJC Scopus subject areas

  • Economics and Econometrics
  • Applied Mathematics

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