Consistent Utility of Investment and Consumption: a forward/backward SPDE viewpoint *

Nicole El Karoui, Caroline Hillairet and Mohamed Mrad ()
Additional contact information
Nicole El Karoui: LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique
Caroline Hillairet: ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris
Mohamed Mrad: LAGA - Laboratoire Analyse, Géométrie et Applications - UP8 - Université Paris 8 Vincennes-Saint-Denis - UP13 - Université Paris 13 - Institut Galilée - CNRS - Centre National de la Recherche Scientifique

Post-Print from HAL

Abstract: This paper provides an extension of the notion of consistent progressive utilities U to consistent progressive utilities of investment and consumption (U, V). It discusses the notion of market consistency in this forward framework, compared to the classic backward setting with a given terminal utility, and whose value function is an example of such consistent forward utility. To ensure the consistency with the market model or a given set of test processes, we establish a stochastic partial differential equation (SPDE) of Hamilton-Jacobi-Bellman (HJB)-type that U has to satisfy. This SPDE highlights the link between the utility of wealth U and the utility of consumption V, and between the drift and the volatility characteristics of the utility U. By associating with the HJB-SPDE two SDEs, we discuss the existence and the uniqueness of a concave solution. Finally, we provide explicit regularity conditions and characterize the consistent pairs of consistent utilities of investment and consumption. Some examples, such as power utilities, illustrate the theory.

Keywords: Market-consistent progressive utility of investment and consumption; Forward/backward stochastic partial differential equation (SPDE) (search for similar items in EconPapers)
Date: 2018-02-15
Note: View the original document on HAL open archive server: https://hal.science/hal-01458419v1
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Published in Stochastics: An International Journal of Probability and Stochastic Processes, 2018

Downloads: (external link)
https://hal.science/hal-01458419v1/document (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: https://EconPapers.repec.org/RePEc:hal:journl:hal-01458419

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().