Economics at your fingertips  

Epstein-Zin Utility Maximization on a Random Horizon

Joshua Aurand and Yu-Jui Huang

Papers from

Abstract: This paper solves the consumption-investment problem under Epstein-Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable, but not necessarily tradable, state processes. Contrary to prior studies, we do not impose any fixed upper bound for the random horizon, allowing for truly unbounded ones. Focusing on the empirically relevant case where the risk aversion and the elasticity of intertemporal substitution are both larger than one, we characterize the optimal consumption and investment strategies using backward stochastic differential equations with superlinear growth on unbounded random horizons. This characterization, compared with the classical fixed-horizon result, involves an additional stochastic process that serves to capture the randomness of the horizon. As demonstrated in two concrete examples, changing from a fixed horizon to a random one drastically alters the optimal strategies.

Date: 2019-03, Revised 2023-05
New Economics Papers: this item is included in nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1) Track citations by RSS feed

Published in Mathematical Finance, Vol. 33 (2023), Issue 4, pp. 1370-1411

Downloads: (external link) Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Access Statistics for this paper

More papers in Papers from
Bibliographic data for series maintained by arXiv administrators ().

Page updated 2024-01-09
Handle: RePEc:arx:papers:1903.08782