Sensitivity of Optimal Consumption Streams

29 Pages Posted: 14 Aug 2015 Last revised: 14 Sep 2017

See all articles by Martin Herdegen

Martin Herdegen

University of Warwick - Department of Statistics

Johannes Muhle-Karbe

Carnegie Mellon University - Department of Mathematical Sciences

Date Written: September 12, 2017

Abstract

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

Herdegen, Martin and Muhle-Karbe, Johannes, Sensitivity of Optimal Consumption Streams (September 12, 2017). Swiss Finance Institute Research Paper No. 15-27. Available at SSRN: https://ssrn.com/abstract=2643322 or http://dx.doi.org/10.2139/ssrn.2643322

Martin Herdegen

University of Warwick - Department of Statistics ( email )

Coventry CV4 7AL
United Kingdom

Johannes Muhle-Karbe (Contact Author)

Carnegie Mellon University - Department of Mathematical Sciences ( email )

Pittsburgh, PA 15213-3890
United States

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