Optimal investment and consumption problems under correlation ambiguity
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AbstractConsider an economy with d stochastic factors that have an ambiguous variance–covariance matrix. An ambiguity- and risk-averse agent seeks to determine the optimal investment and consumption strategy that is robust to the uncertainty in the covariances. We formulate the robust decision rule as an expected utility maximization over the worst-case scenario with respect to all possible covariances. As this variance–covariance ambiguity leads to robust optimal decisions over a set of non-equivalent probability measures, the G-expectation framework is adopted to characterize the problem as a maximin optimization. Our problem formulation can be applied to finite and infinite horizon investment–consumption problems with or without a subsistence consumption constraint. We demonstrate our models using two examples including the defined contribution pension problem and lifetime optimal investment–consumption problems.
All Author(s) ListBingyan Han, Hoi Ying Wong
Journal nameIMA Journal of Management Mathematics
Year2020
Month1
Volume Number31
Issue Number1
PublisherOxford University Press
Pages69 - 89
ISSN1471-678X
LanguagesEnglish-United States
KeywordsConsumption and investment problem, Robust control, Correlation anbiguity

Last updated on 2020-13-10 at 03:38