OPTIMAL INVESTMENT WITH AN UNBOUNDED RANDOM ENDOWMENT AND UTILITY-BASED PRICING

Authors: Owen, MarkP.¹; Žitković, Gordan²

Source: Mathematical Finance, Volume 19, Number 1, January 2009 , pp. 129-159(31)

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Abstract:

This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the existence of an optimal trading strategy within a class of permissible strategies—those strategies whose wealth process is a super-martingale under all pricing measures with finite relative entropy. We give necessary and sufficient conditions for the absence of utility-based arbitrage, and for the existence of a solution to the primal problem. We consider two utility-based methods which can be used to price contingent claims. Firstly we investigate marginal utility-based price processes (MUBPP's). We show that such processes can be characterized as local martingales under the normalized optimal dual measure for the utility maximizing investor. Finally, we present some new results on utility indifference prices, including continuity properties and volume asymptotics for the case of a general utility function, unbounded endowment and unbounded contingent claims.

Keywords: utility maximization; incomplete markets; random endowment; marginal utility-based price processes; utility indifference prices

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.1467-9965.2008.00360.x

Affiliations: 1: Heriot-Watt University 2: University of Texas at Austin

Publication date: 2009-01-01