A large deviations approach to optimal long term investment

Huyên Pham ()
Additional contact information
Huyên Pham: Laboratoire de Probabilités et Modèles Aléatoires, CNRS, UMR 7599, UFR Mathématiques, Case 7012, Université Paris 7, 2 Place Jussieu, 75251 Paris Cedex 05, France

Finance and Stochastics, 2003, vol. 7, issue 2, 169-195

Abstract: We consider an investment model where the objective is to overperform a given benchmark or index. We study this portfolio management problem for a long term horizon. This asymptotic criterion leads to a large deviation probability control problem. Its dual problem is an ergodic risk sensitive control problem on the optimal logarithmic moment generating function that is explicitly derived. A careful study of its domain and its behavior at the boundary of the domain is required. We then use large deviations techniques for stating the value function of this criterion of outperformance management. This provides in turn an objective probabilistic interpretation of the usually subjective degree of risk aversion in CRRA utility function.

Keywords: Large deviation; risk sensitive control; dynamic programming equation; optimal logarithmic moment generating function; benchmark; optimal portfolio (search for similar items in EconPapers)
JEL-codes: D81 G11 (search for similar items in EconPapers)
Date: 2002-12-10
Note: received: June 2001; final version received: May 2002
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.de/link/service/journals/00780/papers/3007002/30070169.pdf (application/pdf)
Access to the full text of the articles in this series is restricted

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:spr:finsto:v:7:y:2003:i:2:p:169-195

Ordering information: This journal article can be ordered from
http://www.springer. ... ance/journal/780/PS2

Access Statistics for this article

Finance and Stochastics is currently edited by M. Schweizer

More articles in Finance and Stochastics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().