Sensitivity of Optimal Consumption Streams
29 Pages Posted: 14 Aug 2015 Last revised: 14 Sep 2017
Date Written: September 12, 2017
We study the sensitivity of optimal consumption streams with respect to perturbations of the random endowment. At the leading order, the consumption adjustment does not matter: any choice that matches the budget constraint simply shifts the original utility by the marginal value of the perturbation. Nontrivial results can be obtained by considering the next-to-leading order. Here, one first solves the problem for a deterministic perturbation, which leads to a "prognosis measure". The desired consumption adjustment for a general endowment perturbation is in turn given by the conditional expectation of the latter, computed under this measure and appropriately weighted with the conditional expectations of the remaining risk-tolerance.
Keywords: optimal consumption, random endowment, asymptotic analysis
JEL Classification: G11, D91, E21
Suggested Citation: Suggested Citation