Occasional Ratcheting: Optimal Dynamic Consumption and Investment Given Intolerance for any Decline in Standard of Living
A constraint that consumption cannot fall over time (or can fall only at a limited rate) can arise directly from preferences or indirectly from internal production considerations. For example, much of a university's budget includes expenditures that must be maintained because of implicit and explicit long-term contracts. Similarly, expenditures on consumer durables are also long-term commitments. This paper analyses optimal consumption and investment for agents whose consumption cannot fall over time. The preferences are time-separable with constant relative risk aversion conditional on consumption never falling, and they can be represented as non-time-separable extended-real-valued von Neumann-Morgenstern preferences unconditionally. Optimal consumption increases each time that wealth achieves a new maximum. Optimal investment at a point in time is similar to constant proportions portfolio insurance, but the dynamics are different due to the form of consumption dynamics. Extensions include bounding the rate of decrease in consumption with a constant other than zero and the placement of a bound on the maximal holding of the risky asset as a proportion of wealth.
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