Optimal investment with an unbounded randon endowment and utility-based pricing

Mark P. Owen, Gordan Žitković

Research output: Contribution to journalArticle

39 Citations (Scopus)

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. © 2009 Wiley Periodicals, Inc.

Original languageEnglish
Pages (from-to)129-159
Number of pages31
JournalMathematical Finance
Volume19
Issue number1
DOIs
Publication statusPublished - Jan 2009

Keywords

  • Incomplete markets
  • Marginal utility-based price processes
  • Random endowment
  • Utility indifference prices
  • Utility maximization

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