Optimal investment and consumption with forward preferences and uncertain parameters

Wing Fung Chong, Gechun Liang

Research output: Contribution to journalArticlepeer-review


We introduce and analyze a class of forward performance criteria in incomplete markets in the presence of model ambiguity. Incompleteness stems from general investment constraints, while model uncertainty is represented by a convex and compact set of plausible model parameter processes. Following the max-min criteria in traditional (backward) robust control, we formulate similar criteria for the robust forward performance processes and focus on the rich class of time-monotone processes. We provide a novel PDE characterization and a semi-explicit saddle-point construction of the robust forward performance criteria and their optimal policies. Furthermore, we present additional results within the class of homothetic constant relative risk aversion (CRRA) processes. Within this class, we investigate the relationship between forward performance processes on wealth and those on consumption, establishing an interesting dominance through time.
Original languageEnglish
Pages (from-to)65-84
Number of pages20
JournalProbability, Uncertainty and Quantitative Risk
Issue number1
Publication statusPublished - Mar 2024


  • Robust forward performance criteria
  • Portfolio constraints
  • Consumption
  • Saddle points
  • Constant relative risk aversion

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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