Optimal Investment with an Unbounded Random Endowment and Utility-Based Pricing

31 Pages Posted: 17 Jan 2009

See all articles by Mark P. Owen

Mark P. Owen

affiliation not provided to SSRN

Gordan Zitkovic

University of Texas at Austin

Date Written: 2007-08

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 strategiesthose 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.

Suggested Citation

Owen, Mark P. and Zitkovic, Gordan, Optimal Investment with an Unbounded Random Endowment and Utility-Based Pricing (2007-08). Mathematical Finance, Vol. 19, Issue 1, pp. 129-159, January 2009, Available at SSRN: https://ssrn.com/abstract=1327439 or http://dx.doi.org/10.1111/j.1467-9965.2008.00360.x

Mark P. Owen

affiliation not provided to SSRN ( email )

Gordan Zitkovic

University of Texas at Austin ( email )

2317 Speedway
Austin, TX 78712
United States

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