Consumption processes and positively homogeneous projection properties

Tom Fischer

Research output: Contribution to journalArticle

Abstract

We constructively prove the existence of time-discrete consumption processes for stochastic money accounts that fulfill a pre-specified positively homogeneous projection property (PHPP) and let the account always be positive and exactly zero at the end. One possible example is consumption rates forming a martingale under the above restrictions. For finite spaces, it is shown that any strictly positive consumption strategy with restrictions as above possesses at least one corresponding PHPP and could be constructed from it. We also consider numeric examples under time-discrete and -continuous account processes, cases with infinite time horizons, and applications to income drawdown and bonus theory. © 2008 Springer-Verlag.

Original languageEnglish
Pages (from-to)357-380
Number of pages24
JournalFinance and Stochastics
Volume12
Issue number3
DOIs
Publication statusPublished - 8 May 2008

Keywords

  • Consumption strategies
  • Income drawdown
  • log-Lévy processes
  • Martingale consumption
  • Positive homogeneity
  • Smooth bonus

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