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Stochastic forward consumption preferences as a random field via infinite horizon BSDEs

Construct forward consumption preferences as a stochastic random field using infinite horizon backward stochastic differential equations (BSDEs), and ascertain the feasibility and conditions for such a construction so that consumption preferences need not be deterministic over time.

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Background

The paper develops robust forward investment and consumption preferences using an ODE-driven deterministic consumption preference process λ. In the conclusions, the authors identify a significant extension: building stochastic forward consumption preferences as random fields by leveraging infinite horizon BSDEs. This would better reflect realistic situations where agents' preferences evolve stochastically and are not purely deterministic, but the construction and analysis are left unaddressed.

References

Secondly, one could investigate the possibility of constructing stochastic forward consumption preferences as a random field using the element of infinite horizon BSDEs. This is undoubtedly a very important extension, since any preferences of the agent are unlikely to be deterministic over time. This mathematically challenging but practically meaningful generalization 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 6 (Concluding Remarks and Future Directions)