Random forward consumption preference process λ

Establish whether non-zero volatility robust randomized CRRA forward investment and consumption preferences can be constructed when the forward consumption preference process λ is stochastic (random) rather than a bounded deterministic function of time, and determine the necessary conditions under which such preferences exist within the incomplete market with drift and idiosyncratic volatility uncertainties.

Background

In constructing robust randomized CRRA forward preferences, the paper assumes the forward consumption preference process λ is a bounded deterministic function of time to ensure tractability and the solvability of the accompanying ODE (15). A parameter condition (16) is imposed to guarantee existence and consistency between investment and consumption preferences. The authors explicitly point out that allowing λ to be random remains unaddressed, indicating a gap in extending the framework to stochastic consumption preference processes.

References

However, we note that the case where λ is random remains an open question and is left for future research.

— Robust forward investment and consumption under drift and volatility uncertainties: A randomization approach (2410.01378 - Chong et al., 2 Oct 2024) in Section 4