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We consider an individual or household endowed with an initial capital and anincome, modeled as a linear function of time. Assuming that the discount rateevolves as an Ornstein-Uhlenbeck process, we target to find an unrestrictedconsumption strategy such that the value of the expected discounted consumptionis maximized. Differently than in the case with restricted consumption rates,we can determine the optimal strategy and the value function.

Unrestricted Consumption under a Deterministic Wealth and an Ornstein-Uhlenbeck Process as a Discount Rate