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How potential investments may change the optimal portfolio for the exponential utility

Schachermayer, Walter (2002) How potential investments may change the optimal portfolio for the exponential utility. Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science", 86. SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, Vienna.

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Abstract

We show that, for a utility function U: R to R having reasonable asymptotic elasticity, the optimal investment process H. S is a super-martingale under each equivalent martingale measure Q, such that E[V(dQ/dP)] < "unendlich", where V is conjugate to U. Similar results for the special case of the exponential utility were recently obtained by Delbaen, Grandits, Rheinländer, Samperi, Schweizer, Stricker as well as Kabanov, Stricker. This result gives rise to a rather delicate analysis of the "good definition" of "allowed" trading strategies H for the financial market S. One offspring of these considerations leads to the subsequent - at first glance paradoxical - example. There is a financial market consisting of a deterministic bond and two risky financial assets (S_t^1, S_t^2)_0<=t<=T such that, for an agent whose preferences are modeled by expected exponential utility at time T, it is optimal to constantly hold one unit of asset S^1. However, if we pass to the market consisting only of the bond and the first risky asset S^1, and leaving the information structure unchanged, this trading strategy is not optimal any more: in this smaller market it is optimal to invest the initial endowment into the bond. (author's abstract)

Item Type: Paper
Keywords: utility maximization / incomplete markets / duality
Classification Codes: JEL G11, G12, C61
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Departments > Informationsverarbeitung u Prozessmanag. > Informationswirtschaft
Departments > Informationsverarbeitung u Prozessmanag. > Produktionsmanagement > Taudes
Departments > Marketing > Service Marketing und Tourismus
Depositing User: Repository Administrator
Date Deposited: 25 Mar 2002 11:42
Last Modified: 09 Apr 2015 15:06
URI: http://epub.wu.ac.at/id/eprint/444

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